Can someone recommend a Lenormand deck that includes extra man and woman cards (and ideally cards for people outside the gender binary) so I can read more easily for LGBTQ people?
Under the Roses by Kendra Hurteau & Katrina Hill has an extra set, as well as an additional child card. They're not outside the gender binary, however. It's a lovely deck, all the same.
None of these have a gender binary card, I can't think of a deck that does. If i were to read for someone who let me know they identified as non-binary I might charge the Stars card for the reading to appear as their signification. This has absolutely no basis in tradition it just stands apart from sun and moon in terms of polarity.
I don't think Lenormand has caught up to the non-gender-binary concept at this time. The extra Man and Woman cards are aimed more at same-sex partnerships, to avoid having to use the Rider as a male partner and the Snake as a female partner. All the decks I'm aware of have two distinctly male or female cards. As Shade says, you can always make your own decision as to which card to use.
The Enchanted Lenormand has an extra man and woman, as well as a card called "The Diviner" which is supposed to represent Mlle. Lenormand herself, but looks very androgynous. I use it for a non-binary significator, or I let the querent choose which card to use to represent themself.