Catalysis of the reaction: 5-carboxymethylaminomethyluridine34 in tRNA(Leu) + S-adenosyl-L-methionine = 5-carboxymethylaminomethyl-2'-O-methyluridine34 in tRNA(Leu) + H+ + S-adenosyl-L-homocysteine.
tRNA (cytidine(34)/5-carboxymethylaminomethyluridine(34)-2\'-O)- methyltransferase activity