If a person is lesbian, does she need cervical cancer jab?

Yes.: Cervical cancer is most commonly caused by infection with human papilloma virus (hpv). Hpv can be transmitted sexually from skin to skin contact between two women. I believe the "cervical cancer jab" you are referring to is gardasil, which is a vaccine against high-risk types of hpv that can cause cervical cancer, and women who have sex with women should receive the vaccine.

Yes: All women and even young men who have not been infected will benefit from hpv vaccine for two reasons: hpv is spread by sexual contact, not just penetrating intercourse. Second it can cause not just cervical, but vaginal, bladder and throat cancers.