Hi Matt,
You will have no problems being gay in Lombok, it is no different than in Bali. Several of the hotels are owned and run by gay men, and there is a small expat gay community. I've holidayed many times with gay men and women, and had gay neighbours, and have never observed any problems for them, nor have they mentioned any.
A couple of words of advice - in Indonesia, men are sometimes seen holding hands but this is not an indication of preference for same sex partners, it is a normal thing between close male hetro friends. Also, be it between same sex or opposite sex, public displays of affection are not part of the culture, so just be discreet.
Indonesian culture (be it Bali, Lombok or elsewhere) does not condone open homosexuality, so most gay locals either stay in the closet, or come out and are shunned by their village and have to move elsewhere, usually to a tourist area which is more tolerant.