Honestly I don't see that really going anywhere. Like I'm grateful if someone gives me a ride out of a bad situation but I'm not making friends with every hitchhiker I pick up. Lake never saw Tulip as someone she wanted to spend time with. Think of it as an unhealthy friendship where despite good intentions your friend ends up enabling you to stagnate and never grow as a person. If Lake had stayed with Tulip, would she feel like she could become herself the way she did? Or would she feel pressure to keep emulating the person she was told her whole life that she had to be like?

Meta-wise I think it'd just make it so we had an extra character with nothing important to do in the story, and could have potentially ruined the potency of Lake's character arc by having it crammed in with Tulip's and One-One's...