To be fair, we don't know that the family gathering is a lie. It might be a lie, but it kind of doesn't matter since if she wanted to go to prom Aya would skip it even if it were true.
As for the rest, I think we're coming up against a disagreement here because Mitsuki never asked Aya about her intentions. She didn't ask if Aya wanted to go, just if she was going. Aya said she wasn't going, not that she didn't want to go.
I agree that Aya is fudging the truth here a bit with implications, but I also can't say I'm super into how Mitsuki just assumes Aya will be her date without asking her or expressing herself. She doesn't say, "Too bad about your family gathering, I'd rather have gone to prom with you than this music event", she just keeps it to her self. And then this chapter she just straight up says "You didn't want to go with me?" as if she had asked Aya and was rejected.
Mitsuki is doing the same thing Joe is doing, assuming that things will just go her way without being explicit. Aya is doing the opposite, assuming things will not go her way which makes her not try. Aya has her own problems to deal with, but let's not discount Mitsuki again not expressing herself.
I generally agree with the last paragraph. I would say though that your "best friend" who you do everything with suddenly going to a large event without telling or inviting you would make most people feel some kind of way.
That's also why Mitsuki doesn't need to ask whether Aya would be going with her. It's an understanding between the two of them already, and we know Aya did indeed plan to go with Mitsuki and no one else.
Mitsuki asking if Aya is going to the prom is Mitsuki asking if they're both going. Aya understands that implication. That understanding is why Aya reacts as she does, pretending she can't and never intended to go, so Mitsuki feels no burden. She knows Mitsuki and her are a two-person deal.
There's an argument for taking someone for granted but these two aren't a couple and we don't even know Mitsuki's romantic feelings, so it's all very muddled. That's part of the issue though. Too much of their relationship is left to assumptions and silent understanding between themselves and to the reader. It's long been time to be more direct between themselves and narratively.
I don't like the idea that Mitsuki doesn't need to ask Aya because it's an understanding between them. To some extent that's been the case so far, but it leads to situations like Joe's and Kanna's.
Looking back at some of their major events:
ch 37 and 38 - RHCP fight
ch 51 - Aya to Mitsuki "You don't talk to me at all, Koga-san. I think that one day, you'll end up going away without telling me. That's how I feel sometimes." Instead of answering, Mitsuki takes her finger in hers.
ch 79 - Mitsuki to Aya "I'm sorry. I mean...this was supposed to be a secret between you and me..." referring to the tattoos and piercings.
ch 97 - After not hearing from her for a week, Mitsuki comes back and actually thanks Aya for getting angry on her behalf.
ch 100 - "The safest place for me...should have been next to you, Oosawa-san." Mitsuki thinks, but doesn't actually say to Aya.
ch 107 - Mitsuki decides to tell Aya about the music industry party invitation, Aya says she's not going to the prom
They do talk sometimes, like they have a moment in ch97 when Mitsuki comes back to school. But largely speaking Mitsuki never really directly addresses the things that Aya says to her, and keeps inside of her how she feels about everything. Even the prom situation. Rather than asking Aya what her prom plans are, she tells her about the music industry party invite first. How could Aya not see that as the primary thing she wants to do, if it's the first thing she brought up?
And Aya doesn't assume they'll go together, she just wants to go with her. Her saying "I'm not going either" doesn't imply they would have gone together, it just says, "don't worry about being the only one to miss out on the prom". If she assumed they would go together, she wouldn't have first asked Narita and she wouldn't have been worried about messing up the timing.