Los Angeles Youth Network
The Los Angeles Youth Network is a shelter for runaway and homeless youth (RHY) aged 12-17. This organization also has a transitional living program for youth aged 18-21.
I was a homeless transgender youth when I was 16 and found this shelter. It was amazing, they are trans friendly. They do house you in your preferred gender and are very good about using your preferred name and pronouns. They are supportive of youth starting hormone replacement therapy, they also assist with family couseling to help you go home. It isn't a LGBT specific organization, but they are very LGBT friendly.