They could have been in bad term with Lisa's parents until their death.
But afterward have taken care of Lisa.
As
Birdnman993 wrote, we still don't know what happen to Lisa after her mother suicide. So we can just speculate for now.
But what we can assume is that someone has taken care of Lisa for the rest of her childhood and adolescence.
I reckon the Foster System. Too many questions would've been raised about the Death, the Neglect, the Abuse, and state the House was in, why Relatives didn't step in, etc.
It's entirely possible that she sat in the house after finding her Mom like that, as we saw she kind of went crazy, perhaps too broken to move. In which case, someone would have found her (or the smell) eventually.
We don't know enough about the Grandparents (from what I remember), but given the state of her Mom not just Mentally but also Financially, she probably would've been taken to her Grandparents far sooner if it was possible, or if they even wanted her.
What's interesting to me is how much of her personal life she's kept hidden up to this point, especially on Social Media; no Family is mentioned there (I think). She probably was eventually Adopted though, unless she presents herself WAY better than I gave her credit for, beyond just the smile, which again, is entirely possible.
But that's all just my two cents on the matter, I could be entirely wrong. I reckon we'll find out in her Path.
The real question is, will she become a possible
Yandere for us later down the line??? You know for
saving her life and being the first person to listen to her in...I dunno, ages? Kinda hope so, Yanderes in the Well Written 3D space are a Rare Breed I so desperately crave, and she has the potential for it, it would make sense if she did, Mental Health speaking. Though I guess Jogger Girl is closer to that Category, given how clingy she is with us.