I don't think they should.
It has been established that Lola's mum is not going to win any prizes for her parenting, or Lola would not be in care. We have seen the same thing with Whitney, her mother was the strereotypical bad mum, I thought she was addicted to probably somehting worse than booze, and was selling ehrself to get it, or at the very least didn't get the meas to that end in any legal way. She clearly didn't give a toss about ehr daughter. I fully expect Lola's mum to be the same. Been there, seen that.
Also, Lola works just fine with Billy for a dad and Cora for a mum, or that is what it comes down to, she doesn't need anyone else.
Maybe in a few years, should Lol get separated from Billy or Cora and her friends somehow, or something else comes up, like a disease that may run in the family and she wants to go and ask her mother about it.
Personally, I think the only way to make it work, should her mother ever come in it, is to give her some sort of mental disorder, maybe schizophrenia or borderline or something. That way, it could be explained why she couldn't look after Lola, especially if she wasn't diagnosed yet, or only just and gradually got better over time. Just like Jean is a nice person, but she isn't always capable of looking after a child. Lola, being very young now, would have had even more trouble understandign her mum's behaviour back then, nor why it may have been for the best to get her out of that house, especially if nobody knew the source of it, and/or nobody told Lola, as she was just a kid who wouldn;t understand anyway. Then they could rebuild there relationship when mummy dearest gets back..
The only problem with that plan is that it is at a high risk of becoming Stacey and Jean 2.0, especially since Lola is a little similar to young Stacey, at least when she first arrived.