Well it's not like anybody demanded Lilia to raise her daughter that way. She got a lot of autonomy in raising her child, and they ultimately treated her more like a 2nd wife rather than a maid.
Her backstory from the very beginning does a good job of showing that she has a lot to owe from becoming a maid. She had to retire early due to a bad injury, and she probably would've been homeless if not for Paul accepting her in, where she eventually found happiness from Rudeus defending her. In the WN, they go into a bit more about her mindset at the time, that she was fully prepared to throw away her happiness and maybe even resort to prostitution if Zenith decided to kick her out.
So I think Lilia in her own twisted way thinks that even if her daughter is a genius, she'd still be happier serving somebody like Rudeus as a maid rather than have the perilous life Lilia formerly led.