This should be close imo.
By the end Elfen Lied Lucy was pretty powerful, easily at city level in terms of destruction.
That's her vectors destroying several buildings and she destroyed several ships out at sea in another scan. In the 2nd scan you can see that each of her vectors are pretty much city level buster in size but because of the massive energy required to use such an attack it effectively killed her too so that would have to be a real desperate attack.
The above scans don't have much to do with this thread, just wanted to show what Lucy can do at peak :)
Mew's not really shown any impressive attacks though but was easily keeping up with Mewtwo who in an earlier video I posted was shown creating an explosion that pretty much engulfed an island. That was without even straining too much.
Overall though if Mew can dodge her vectors, either via actually dodging them or they are unable to get past his force field, then using a psychic attack then he should be able to take this. As far as I am aware Lucy has no way do defend against psychic attacks but I don't really remember much about Elfen Lied. Otherwise Lucy's going to chop Mew into little pieces.
It's going to really come down to whoever can attack first though and personally I think Psychic would reach Lucy before her Vectors reached Mew.