You are approaching this from the wrong angle. Instead of asking how to deal with Lemon, you should be asking if they are correct, and how to move forward with that information.

In this case, the argument basically boils down to you saying that gender & sexuality are personality traits, while Lemon is saying that they are not Personality Traits. While the former can be debated in the real world (I am not getting into that), the latter is true according to the rules, which makes it relevant to the resolution of this question.

Now, you have said that your group did use a variant of Inspiration previously, under a different GM, and that Lemon as GM has not used Inspiration before. This is relevant due to the connection between Inspiration and Personality Traits, Ideals, Bonds, and Flaws, under the standard rules for awarding Inspiration.

Further, you have made it very clear that sexual identity and preference are very prominent in your character creation, but have also indicated that personality quirks (traits under a different name) tend to get left out. Lemon may want you to have more clear quirks for them to reference and consider.

Last, because they are likely arguing based upon the Rules as Written, and they are acting as GM, they are well within their rights to want your sheets to comply with those rules, which would make it easier for them to reference your sheets, and run the game.

So, what you should do, is ask (to be sure) if you can have the information for sexual identity and preference on your sheets, under a different section; then get help with good Personality Traits to fill in. This may be a small burden for yourselves as players, but could be a great help for Lemon to GM smoothly, making things run better for your group.

You need to simply ask Lemon if he intends to use standard rules for Personality Traits and Inspiration, then work with him as your GM if he does.

Given that you have stated that Lemon tends to argue for RAW, him arguing a position consistent with RAW is likely based on intent to use the rules in this way.

It does not matter that your group(Lemon included as player) has used variant Inspiration rules previously, and it does not matter that your group has used homebrew Personality Trait rules previously either, what matters is that Lemon(as GM) wants to try standard Personality Trait rules.

Understand, I am not saying Lemon's opinion is all that matters, your opinions as players matter too, but you need to step back and look at the situation objectively: is he saying your characters cannot be as you want them? No. Is he saying you cannot have the info you want on your sheets? No. He is simply saying that sexual interest and identity dont go in the Personality Traits section.

Also understand, you can differ of opinion with Lemon on the discussion of sexuality and personality in real life, and have that discussion be completely irrelevant to the rules and structure of the game. Remember: this game is not real life.

Further, consider how jarring it is to change mediums in communications. You encounter situations which are frustrating, and that frustration can lead someone to acting more aggressively for a time. Not to mention, everyone handles different mediums and circumstances differently, some people are very clear in person, but have difficulty online, others are the opposite. Perhaps Lemon is just having more difficulty from this.

Last, consider that there may be circumstances in Lemon's life which could lead to more confrontation, whether he recognizes these or not. (Think of how it feels when you are persecuted, and consider that Lemon may be feeling similar).