
Yes, but that's kind of the point. And Lyle acknowledged that he was in wrong. Unfortunately he was in a rlly emotional state at the time like you said and I feel like Ash coming in and trying to talk to him made him explode ;[ If he had more time to himself in that room I think he could've handled the situation better. But that's not the case here because they need some sort of conflict to finally face their insecurities, they can't just have a perfect healthy relationship without first handling that.

We can't forget this is an omegaverse .. so seeing it from that perspective it makes sense he's reacting this way .. specially the bond part when it has such an impact and importance in that "type?" of society ..
Still you can see and appreciate the fact that they truly respect and care for each other , Lyle knows his way of thinking is all over the place and decided on his own to confront those thoughts and emotions , and Ash gave his partner the space and time till he was ready..
Did Lyle overreact? Totally, but it's obvious the author was looking for that kind of drama
But this is just my 2 cents

Its in character for Karlyle to react that way plus its fine, he's still so new to love and lots of new lovers even in irl have this situation happen
It would have been a big problem if Karlyle went back to his roots of keeping silent but atleast the big improvement is that hes actively making a decision to quickly apologize and listen to Ash's explanation after he realized his mistake
Ash had a failed relationship, Karlyle never had one both wont have any healthy relationship habits when its still early
Lyle reaction is a bit… annoying. Now let me explain.
I can understand that you might argue, Ash should’ve told him first or something along that line but if you TRULY cares about your partner, you will try to find a way to understand them.
Now, what I meant is, if Ash didn’t bring it up it could’ve been something he doesn’t want to talk about in the first place and as his partner, Lyle has the right to ask but doesn’t have the right to pry. Now is being emotionally affected by such news realistic? Yes. But since we all know how much they love each other, I would have love to see them practice in healthy relationships between them.
Imagine if Lyle thought things through and try and ask Ash instead of listening in until he got consumed by his feelings? I would’ve love to see that honestly, because this is a side story and we got to see how their relationship has change them into an understanding person.
Of course this is just MY take on this side story, I still love Lyle with my whole heart even if that one scene annoys me.