Bi? Who says she cares at all about dudes?
Anyway, Lili's a sheltered, overprotected girl, so Asuka was probably the first friend she's made. Certainly the first one able to rival her in battle. Therefore she goes to great lengths to be acknowledged by her and to provoke her into a fight, as shown by her ending. Whether her obsession also ventures into the realm of sexual attraction is up to the viewer, though I'm certainly not against the idea. They do make for one adorably sexy couple.