Protein-lysine methyltransferase that efficiently catalyzes three successive methylations on 'Lys-36' in eukaryotic translation elongation factor 1 alpha (EEF1A1 or EEF1A2). L-lysyl-[protein] + S-adenosyl-L-methionine = H(+) + N(6)-methyl-L-lysyl-[protein] + S-adenosyl-L-homocysteine N(6)-methyl-L-lysyl-[protein] + S-adenosyl-L-methionine = H(+) + N(6),N(6)-dimethyl-L-lysyl-[protein] + S-adenosyl-L-homocysteine N(6),N(6)-dimethyl-L-lysyl-[protein] + S-adenosyl-L-methionine = H(+) + N(6),N(6),N(6)-trimethyl-L-lysyl-[protein] + S-adenosyl-L-homocysteine Belongs to the methyltransferase superfamily.