I cannot recruit Lilly. I read that you should talk with the guys who gives you the special sword for which you donated before. But nothing happens.
First time I had to go to the institute he gave me the sword. I didn't remember if it should have been taken in LF2. I play LF3 with another man's save. The second time, after Titanic, again no reaction from him. And it was said he should do something about Lilly's bazooka.