There are a few things here. Let me first say that Pan is an excellent choice for sexuality of any type. Other patrons that I would suggest for Lesbians are:
The most obvious would be Lesvos: Patron God of the Island of Lesbos, which Sappho wrote about and from which we get the word Lesbian, much to the chagrin of the people who still live there. I know a certain 60 year old Greek dude who would love to stand up and proudly proclaim himself a Lesbian without evoking giggles. Of course, there is not a lot of info on Lesvos as a diety, but here are a couple other choices:
Baubo: Greek Goddess of Baudy Humor. She allegedly cheered up Demeter with some dirty jokes than broke her divine depression by lifting her skirt and showing her nether region. Some have suggested this was just humor, some suggest that Baubo had male genitalia, but some suggest that Baubo turned Demeter on, and this was a coded Lesbian act.
Britomartis: also known as Dictynna is another Goddess that is viewed by some as a Lesbian. Whether she was or wasnt no one can say for sure, but there are a lot of mythological indicators that she was a lover of Artemis. She also allegedly showed her disdain of heterosexual love by fleeing from the affections of King Midos and throwing herself off a cliff to get away from him. The fact that Sappho is said to have died the same way is yet another idicator that there is a bit of a secret tradition going on here.
Now as to the deeper question that was asked, whether or not Gods change or reincarnate.
First, I would be remiss if I did not point out that Buddhism posits that Dieties of various pantheons all exist, but are still subject to rebirth. Beings of the Deva realm may be powerful and sublime beyond human understanding. They may live for hundreds of millions of years, this giving the appearance of omnipotence, but they are in the end subject to re-birth in a lower realm. Thus a god or goddess may one day find itself a lowly and suffering hell-being, a starving preta (hungry ghost), an animal, or even a human.
But that type of change is really something that I see as an allegory, not something I interpret literally. Even if it was literal, Dieties life span is longer than humanity has been around, so its an irrelivant point to your problem.
So the more immediate question is does the nature of dieties change over time?
Not an easy one.
The first thing to realize is that the nature of dieties is not only more than we know, but more than we can know without becoming dieties ourselves. They exist and travel fully not only in dimensions of space like we do, but time, probability, and consiousness. Thus dieties have not only multiple futures but multiple pasts. Many (though not all) exist in cosmically transcendant as well as manifestly immanent aspects.
In the the transcendent sense, no, dieties do not change to fit time and culture. If they did, they wouldnt be transcendent.
In the immanent sense, yes, clearly they do. You can look at history and see this. Hekate was originally an anatolian Solar Goddess. She than morphed into sort of a minor Greek Goddess of roads, childbirth, protection and all sorts of things. Later she took on the chthonic aspects of the underworld and witchcraft and so on. Still later she manifests as a fully transcendent being in the Chaldean Oracles.
Even YHVH can be seen to evolve like this. In the YHVH narrative we have a very specific diety of justice and war. Later he gets identified with El in the Elohist narrative that gets intertwined in the Pentatauch making him a much more Universal diety, albeit one that still demands specific sacrifices and specific rules. By the time of the Babylonian captivity you see the prophets Jeremiah and Ezekiel actually declairing the changes in God thinking of how to relate to his people in a less regimented and more individual fashion.
For advice on how to relate to dieties directly, see my post here
I would only add that if the diety you are relating to has a thriving cultus prevalent in a specific culture (ie: Santeria, Vodou, Christianity, Yezidism, Buddhism, etc) than you should make every attempt to relate through fairly orthodox means.
If not than you should make every attempt to study the history and symbolism of that deity, than rely upon direct experience to flesh it out. Do not disregard history and tradition in favor if your vision, the astral can be a place of deception as easily as it is a place of illumination. Do not disregard vision in favor of history either, just make sure that your vision is genuine. Do not create a diety out of wishful thinking. It is IMO a bit of a stretch to say that Pan is now a Lesbian. If anything Pan is Omnisexual and would make an excellent sexual psychopomp/patron no matter what your sexual orientation.
With all that said, I would just like to add that in my own personal opinion all this stuff about dieties is a bit over-rated. Meditate, Elevate, and realize the Diety within.