There are various categories of "insane," and Lulu's mechanism has definitely gone, but she's still functional with a rifle and loyal to the Pitt raider cause. Excitable, she treats you as a pet, even giving you food if you play along with her addled mind.[1]
Lulu roams Uptown's walkways, praising Lord Ashur and handing out noodles. She constantly refers to herself in the third person and addresses all others as "Pet," the reason being "We're all pets of Lord Ashur".