Catalysis of the reaction: S-adenosyl-L-methionine + cytochrome c L-lysine = S-adenosyl-L-homocysteine + cytochrome c N6-methyl-L-lysine. This is the addition of a methyl group to the N6 atom of a lysine residue in cytochrome c.
S-adenosyl-L-methionine:cytochrome c-L-lysine 6-N-methyltransferase activity