In truth, Zero had been see-sawing between staying and going.
His heart had been torn into two different directions and that was why he decided to follow his mother home. Partly to ensure that she was safe and partly, like what Lianne had pointed out, to get to know his roots.
He didn't want to bring Lily for two reasons. One, to keep her safe, and two: if she was here, he would have a reason to return.
Whilst it was true that Lianne had told him to ask her and give her the choice, he was still hesitant about doing so.
He still adopted the 'wait and see' attitude.
Why should he ask her, if he wasn't sure he was going to stay?
While before, it had been that he wouldn't ask because he, himself, could not make that choice; now, it was more of 'I will only ask after I know what I want to do'. There is no point in disrupting her life or cause her unnecessary troubles for something that may not even happen.