5 per update to post, can simply return outside of 0-261 range; deleted 2 characters in body

# Julia, 129129 120 bytes * 0.6 = 77.472

i->(i=big(i);n=0;d=digits;while d(i)!=reverse(d(i))&&n<262 t=BigInt(join(d(i)));println(i," + ",t," = ",i+=t);n+=1end;n>261?-1:n;n+=1end;n)


This creates an unnamed function which takes an integer as input and returns an integer, meanwhile printing each step. Lychrel candidates have a return value of -1262. To call this, give it a name, e.g. f=i->....

function f(i)
# Convert the input to a big integer
i = big(i)

# Initialize a step counter to 0
n = 0

# While the number is not a palindrome and we haven't exceeded 271261 steps...
while digits(i) != reverse(digits(i)) && n < 262

# Get the reverse of the integer
# Note that we aren't using reverse(); this is because digits()
# returns an array of the digits in reverse order.
t = BigInt(join(digits(i)))

# Print the step and increment i
println(i, " + ", t, " = ", i += t)

# Count the step
n += 1
end

# Identify Lychrel candidates by -1,Return otherwisethe returnnumber n
of steps or 262 nfor >Lychrel 271candidates
? -1 : n
end

julia> f(286)
286 + 682 = 968
968 + 869 = 1837
1837 + 7381 = 9218
9218 + 8129 = 17347
17347 + 74371 = 91718
91718 + 81719 = 173437
173437 + 734371 = 907808
907808 + 808709 = 1716517
1716517 + 7156171 = 8872688
8872688 + 8862788 = 17735476
17735476 + 67453771 = 85189247
85189247 + 74298158 = 159487405
159487405 + 504784951 = 664272356
664272356 + 653272466 = 1317544822
1317544822 + 2284457131 = 3602001953
3602001953 + 3591002063 = 7193004016
7193004016 + 6104003917 = 13297007933
13297007933 + 33970079231 = 47267087164
47267087164 + 46178076274 = 93445163438
93445163438 + 83436154439 = 176881317877
176881317877 + 778713188671 = 955594506548
955594506548 + 845605495559 = 1801200002107
1801200002107 + 7012000021081 = 8813200023188
23

julia> f(1186060307891929990)
(steps omitted)
261

julia> f(196)
(steps omitted)
-1262

julia> f(11)
0


# Julia, 129 bytes * 0.6 = 77.4

i->(i=big(i);n=0;d=digits;while d(i)!=reverse(d(i))&&n<262 t=BigInt(join(d(i)));println(i," + ",t," = ",i+=t);n+=1end;n>261?-1:n)


This creates an unnamed function which takes an integer as input and returns an integer, meanwhile printing each step. Lychrel candidates have a return value of -1. To call this, give it a name, e.g. f=i->....

function f(i)
# Convert the input to a big integer
i = big(i)

# Initialize a step counter to 0
n = 0

# While the number is not a palindrome and we haven't exceeded 271 steps...
while digits(i) != reverse(digits(i)) && n < 262

# Get the reverse of the integer
# Note that we aren't using reverse(); this is because digits()
# returns an array of the digits in reverse order.
t = BigInt(join(digits(i)))

# Print the step and increment i
println(i, " + ", t, " = ", i += t)

# Count the step
n += 1
end

# Identify Lychrel candidates by -1, otherwise return n
n > 271 ? -1 : n
end

julia> f(286)
286 + 682 = 968
968 + 869 = 1837
1837 + 7381 = 9218
9218 + 8129 = 17347
17347 + 74371 = 91718
91718 + 81719 = 173437
173437 + 734371 = 907808
907808 + 808709 = 1716517
1716517 + 7156171 = 8872688
8872688 + 8862788 = 17735476
17735476 + 67453771 = 85189247
85189247 + 74298158 = 159487405
159487405 + 504784951 = 664272356
664272356 + 653272466 = 1317544822
1317544822 + 2284457131 = 3602001953
3602001953 + 3591002063 = 7193004016
7193004016 + 6104003917 = 13297007933
13297007933 + 33970079231 = 47267087164
47267087164 + 46178076274 = 93445163438
93445163438 + 83436154439 = 176881317877
176881317877 + 778713188671 = 955594506548
955594506548 + 845605495559 = 1801200002107
1801200002107 + 7012000021081 = 8813200023188
23

julia> f(1186060307891929990)
(steps omitted)
261

julia> f(196)
(steps omitted)
-1

julia> f(11)
0


# Julia, 129 120 bytes * 0.6 = 72

i->(i=big(i);n=0;d=digits;while d(i)!=reverse(d(i))&&n<262 t=BigInt(join(d(i)));println(i," + ",t," = ",i+=t);n+=1end;n)


This creates an unnamed function which takes an integer as input and returns an integer, meanwhile printing each step. Lychrel candidates have a return value of 262. To call this, give it a name, e.g. f=i->....

function f(i)
# Convert the input to a big integer
i = big(i)

# Initialize a step counter to 0
n = 0

# While the number is not a palindrome and we haven't exceeded 261 steps...
while digits(i) != reverse(digits(i)) && n < 262

# Get the reverse of the integer
# Note that we aren't using reverse(); this is because digits()
# returns an array of the digits in reverse order.
t = BigInt(join(digits(i)))

# Print the step and increment i
println(i, " + ", t, " = ", i += t)

# Count the step
n += 1
end

# Return the number of steps or 262 for Lychrel candidates
n
end

julia> f(286)
286 + 682 = 968
968 + 869 = 1837
1837 + 7381 = 9218
9218 + 8129 = 17347
17347 + 74371 = 91718
91718 + 81719 = 173437
173437 + 734371 = 907808
907808 + 808709 = 1716517
1716517 + 7156171 = 8872688
8872688 + 8862788 = 17735476
17735476 + 67453771 = 85189247
85189247 + 74298158 = 159487405
159487405 + 504784951 = 664272356
664272356 + 653272466 = 1317544822
1317544822 + 2284457131 = 3602001953
3602001953 + 3591002063 = 7193004016
7193004016 + 6104003917 = 13297007933
13297007933 + 33970079231 = 47267087164
47267087164 + 46178076274 = 93445163438
93445163438 + 83436154439 = 176881317877
176881317877 + 778713188671 = 955594506548
955594506548 + 845605495559 = 1801200002107
1801200002107 + 7012000021081 = 8813200023188
23

julia> f(1186060307891929990)
(steps omitted)
261

julia> f(196)
(steps omitted)
262

julia> f(11)
0

4 added 71 characters in body

Both bonuses! :D

This creates an unnamed function which takes an integer as input and returns an integer, meanwhile printing each step. Lychrel candidates have a return value of -1. To call this, give it a name, e.g. f=i->....

Note that omitting code relating only to the bonuses, this solution would be 84 bytes.

Both bonuses! :D

This creates an unnamed function which takes an integer as input and returns an integer, meanwhile printing each step. Lychrel candidates have a return value of -1. To call this, give it a name, e.g. f=i->....

This creates an unnamed function which takes an integer as input and returns an integer, meanwhile printing each step. Lychrel candidates have a return value of -1. To call this, give it a name, e.g. f=i->....

Note that omitting code relating only to the bonuses, this solution would be 84 bytes.

3 Thanks to Geobits, + removed storage of BigInt

# Julia, 133129 bytes * 0.6 = 7977.84

i->(B=BigInt;i=Bi=big(i);n=B();d=digits;while;n=0;d=digits;while d(i)!=reverse(d(i))&&n<262 t=Bt=BigInt(join(d(i)));println(i," + ",t," = ",i+=t);n+=1end;n>261?-1:n)


This creates an unnamed function which takes an integer as input and returns a bigan integer, meanwhile printing each step. Lychrel candidates have a return value of -1. To call this, give it a name, e.g. f=i->....

function f(i)
# Convert the input to a big integer
i = BigIntbig(i)

# Initialize a bigstep integercounter to 0 as a step counter
n = BigInt()0

# While the number is not a palindrome and we haven't exceeded 271 steps...
while digits(i) != reverse(digits(i)) && n < 262

# Get the reverse of the integer
# Note that we aren't using reverse(); this is because digits()
# returns an array of the digits in reverse order.
t = BigInt(join(digits(i)))

# Print the step and increment i
println(i, " + ", t, " = ", i += t)

# Count the step
n += 1
end

# Identify Lychrel candidates by -1, otherwise return n
n > 271 ? -1 : n
end


Saved 2 bytes thanks to Geobits!

# Julia, 133 bytes * 0.6 = 79.8

i->(B=BigInt;i=B(i);n=B();d=digits;while d(i)!=reverse(d(i))&&n<262 t=B(join(d(i)));println(i," + ",t," = ",i+=t);n+=1end;n>261?-1:n)


This creates an unnamed function which takes an integer as input and returns a big integer, meanwhile printing each step. Lychrel candidates have a return value of -1. To call this, give it a name, e.g. f=i->....

function f(i)
# Convert the input to a big integer
i = BigInt(i)

# Initialize a big integer to 0 as a step counter
n = BigInt()

# While the number is not a palindrome and we haven't exceeded 271 steps...
while digits(i) != reverse(digits(i)) && n < 262

# Get the reverse of the integer
# Note that we aren't using reverse(); this is because digits()
# returns an array of the digits in reverse order.
t = BigInt(join(digits(i)))

# Print the step and increment i
println(i, " + ", t, " = ", i += t)

# Count the step
n += 1
end

# Identify Lychrel candidates by -1, otherwise return n
n > 271 ? -1 : n
end


# Julia, 129 bytes * 0.6 = 77.4

i->(i=big(i);n=0;d=digits;while d(i)!=reverse(d(i))&&n<262 t=BigInt(join(d(i)));println(i," + ",t," = ",i+=t);n+=1end;n>261?-1:n)


This creates an unnamed function which takes an integer as input and returns an integer, meanwhile printing each step. Lychrel candidates have a return value of -1. To call this, give it a name, e.g. f=i->....

function f(i)
# Convert the input to a big integer
i = big(i)

# Initialize a step counter to 0
n = 0

# While the number is not a palindrome and we haven't exceeded 271 steps...
while digits(i) != reverse(digits(i)) && n < 262

# Get the reverse of the integer
# Note that we aren't using reverse(); this is because digits()
# returns an array of the digits in reverse order.
t = BigInt(join(digits(i)))

# Print the step and increment i
println(i, " + ", t, " = ", i += t)

# Count the step
n += 1
end

# Identify Lychrel candidates by -1, otherwise return n
n > 271 ? -1 : n
end


Saved 2 bytes thanks to Geobits!

2 Both bonuses!
1