Akira's overreactions aren't funny. He's like a protagonist straight from the Heisei era with these weak-kneed shenanigans unbefitting of Reiwa. The praying scene was so wholesome. Cinnamon roll Aoi deserves to be happy after her irresponsible parents ditched her.
Thinking his mother would get mad at him for getting a girlfriend? Did he time travel from the 50s or something? Please.
Now he says Aoi is his girlfriend. Better turn that lie into reality because all he did was delay parental wrath by lying, they'll still get upset at him once they learn the truth even if he comes clean years later. Besides, Aoi's already approved by her future mother-in-law...
But I got a feeling that lie is already busted given his mother must have had time to check the house out and see Aoi's belongings. I think Aoi is going to come clean with the truth here. Akira can lie to his mother, but Aoi lying to her prospective future mother-in-law is going to land her in hotter water than him once they get found out.
In any case, using Akira's lie they can't have Aoi sleep there (a really poorly thought out lie, Akira) so I really think she will tell the truth.