So the word "gay" being used in that context is thought to have originated among gay males to refer to themselves in the early 1900's.

The word "lesbian" being used to refer to homosexual females became popular in the late 1800's, although it had taken other meanings before that. The word comes from the ancient female poet Sappho of Lesbos, who often wrote of her relationships with women. The word "sapphic" also comes from her name. Kinda baller that two popular terms for "homosexual" come from one woman's name, if you ask me.

I don't know why "gay" became the umbrella term for both males and females. Likely, it's because in the English language, masculine terms are more often than not used for gender neutral terms as well (like saying "you guys," for example).