Is Liam cheating on his wife ...?
His character is difficult to assess.
On the Good Wife Route, when his wife takes full care of him, he is a loving man.
He's just incredibly ambitious about wanting to go straight to his brother-in-law.
He wants to know that his family is taken care of, but that is the real reason that drives him.
The cracks show up on the Filthy Route.
He is also incredibly ambitious in his career. Here, too, the driving force is his ambition.
Without the protection of his wife he is careless (gaming problem).
He comes across as naive and overestimates himself and his ability to solve the problem with Morello.
He goes to these meetings incredibly carefree. Believes to be in control of the situation.
On the first thumbnail of the visit to the casino, which L&P later revised, he is incredibly relaxed.
And he's not very emphatic, he doesn't understand why his wife doesn't want sex.
Where the evening went so well for both (him).
I don't know if these are the developer's intended hints. Maybe just my imagination.
But if he cheats on her, and he will, he will for these very reasons. Because she refused him.
And Sophia won't be able to defend herself because she is cheating on him too.