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#Haskell, 59, 57, 56, 52, 51 bytes

l a=2*mod a 2:scanl(+)1(l a)
f n=[l i!!i|i<-[0..n]]

Series definition adapted from this answer.

Less golfed:

fibLike start = start : scanl (+) 1 (fibLike start)
whichStart i = (2*mod i 2)
lucasNacci i = fibLike (whichStart i) !! i
firstN n = [ lucasNacci i | i <- [0..n]]

fibLike start gives an infinite list, defined: f(0)=start, f(1)=1, f(n)=f(n-1) + f(n-2). whichStart i returns 2 for odd input (Lucas series) or 0 for even (Fibonacci series). lucasNacci i gives the ith Lucas-nacci number. firstN n maps over the list.

One byte saved by Boomerang.

#Haskell, 59, 57, 56, 52, 51 bytes

l a=2*mod a 2:scanl(+)1(l a)
f n=[l i!!i|i<-[0..n]]

Series definition adapted from this answer.

Less golfed:

fibLike start = start : scanl (+) 1 (fibLike start)
whichStart i = (2*mod i 2)
lucasNacci i = fibLike (whichStart i) !! i
firstN n = [ lucasNacci i | i <- [0..n]]

fibLike start gives an infinite list, defined: f(0)=start, f(1)=1, f(n)=f(n-1) + f(n-2). whichStart i returns 2 for odd input (Lucas series) or 0 for even (Fibonacci series). lucasNacci i gives the ith Lucas-nacci number. firstN n maps over the list.

One byte saved by Boomerang.

#Haskell, 59, 57, 56, 52 bytes

l a=a:scanl(+)1(l a)
f n=[l(2*mod i 2)!!i|i<-[0..n]]

Series definition adapted from this answer.

Less golfed:

fibLike start = start : scanl (+) 1 (fibLike start)
whichStart i = (2*mod i 2)
lucasNacci i = fibLike (whichStart i) !! i
firstN n = [ lucasNacci i | i <- [0..n]]

fibLike start gives an infinite list, defined: f(0)=start, f(1)=1, f(n)=f(n-1) + f(n-2). whichStart i returns 2 for odd input (Lucas series) or 0 for even (Fibonacci series). lucasNacci i gives the ith Lucas-nacci number. firstN n maps over the list.

#Haskell, 59, 57, 56, 52, 51 bytes

l a=2*mod a 2:scanl(+)1(l a)
f n=[l i!!i|i<-[0..n]]

Series definition adapted from this answer.

Less golfed:

fibLike start = start : scanl (+) 1 (fibLike start)
whichStart i = (2*mod i 2)
lucasNacci i = fibLike (whichStart i) !! i
firstN n = [ lucasNacci i | i <- [0..n]]

fibLike start gives an infinite list, defined: f(0)=start, f(1)=1, f(n)=f(n-1) + f(n-2). whichStart i returns 2 for odd input (Lucas series) or 0 for even (Fibonacci series). lucasNacci i gives the ith Lucas-nacci number. firstN n maps over the list.

One byte saved by Boomerang.

#Haskell, 59, 57, 56, 52 bytes

l a=a:scanl(+)1(l a)
f n=[l(2*mod i 2)!!i|i<-[0..n]]

Series definition adapted from this answer.

#Haskell, 59, 57, 56, 52 bytes

l a=a:scanl(+)1(l a)
f n=[l(2*mod i 2)!!i|i<-[0..n]]

Series definition adapted from this answer.

Less golfed:

fibLike start = start : scanl (+) 1 (fibLike start)
whichStart i = (2*mod i 2)
lucasNacci i = fibLike (whichStart i) !! i
firstN n = [ lucasNacci i | i <- [0..n]]

fibLike start gives an infinite list, defined: f(0)=start, f(1)=1, f(n)=f(n-1) + f(n-2). whichStart i returns 2 for odd input (Lucas series) or 0 for even (Fibonacci series). lucasNacci i gives the ith Lucas-nacci number. firstN n maps over the list.