Medicare provides Caregivers for free. You do not have to take whomever they send, you can choose your caregiver (a friend). If you are a client of the LA LGBTQ CENTER they MAY have a listing of caregivers. Another approach would be to post a sign at the center looking for a LGBTQ Caregiver. Best if luck in your search
Im sure they can put you in touch with the right agency to help you out.
I wish I knew of a good agency. You might want to call The LGBT Center. They just might know. Best Wishes to you and your sister.
Thanks! Your answer is awaiting moderation.