Crossposting from NSFW, because what I have written so far is fairly tame:
For a brief time at the school Sarah Livsey attended, it was fashionable for girls to be into Wicca, as a side effect of a movie about Myrddin being more popular than expected. Sarah being implied by Lisa to have been the popular type, she went in for it, and while she didn't believe it, she had some fun.
Sadly, the butterflies from this did not prevent her brother from trying to kill himself, but it did change the method and results, as he ended up in a coma. Thus, Sarah was not focused on why he did it, but on how to wake him up, and therefore became a Tinker, rather than a Thinker - specifically, a Witchcraft themed Tinker (that doesn't mean she can do magic, just that the method and results of her Tinkering look like witchcraft). She crafted a potion of wakefulness, and time can go down a few branches from there: perhaps it works more-or-less perfectly, and she gets to ask him what the hell he was thinking (which may result in him being angry at her and trying to kill himself, again, using a method she can't bring him back from); perhaps there was some brain damage, and he has amnesia, or other problems; perhaps there was too much brain damage, and she simply can't fix it. One last option is that her parents turned his life support systems off already, and he's been dead for too long. They didn't even talk to her about it (which fits what little we know of there character).
In any event, this isn't going to change the kind of people her parents seem to be, so I could see her running again, it's just that she may be running with her brother, instead of alone.
This is more of the SFW branch of the idea, as the NSFW version is taking a while to get into writable form. BTW, any suggestions for a cape name for this Lisa, other than Witch-Girl or
Wicce?
A number of the branches off this idea still lead to Sarah running, and what brought her to Brockton Bay in canon still might (though this is more likely if she's alone). However, Coil's recruitment methods are reasonably likely to be different: a Thinker who sucks in combat and has a power that tells her how screwed she really is can be recruited with simple brute force, but a Tinker with an eccentric theme who isn't
focused on combat, but can make a good accounting of herself if need be, and still has a few of the 'magic items' that she made with her parents' money, requires different methods. Coil being Coil, he's likely to still be too aggressive when he eventually succeeds, and she'll probably end up hating him, but maybe not as fast or as much.
Likewise, the Undersiders' methods and jobs are going to be different when they have a witchy Tinker instead of a bitchy Thinker, so while they might still end up pissing off Lung, having something like the canon Lung fight occur would rather stretch credibility. How they meet Taylor is thus
very likely to be different. In fact, while the butterflies from this won't prevent the bullying (which started before Sarah even triggered, I think), they might alter the trigger event, and thus Taylor's powers... or they might not. The same is true for Dinah, who may have triggered as late as a week or two before the bank job and kidnapping.
One possibility I've been considering for an alternate meeting with the Undersiders is an effect of one of the direct advantages of having a Tinker on your team: the equipment they might share. In this case, Lisa made a new dog-mask for Bitch, which has various powers. One of the most important is a 'charm' built into the nose, which gives the user something close to a dog's sense of smell, and effectively gives Bitch something a little like Tattletale's canon power, at least for personal interaction (it isn't going to let her sniff out your password - though Lisa could probably make something to let her divine it - but she's going to know how you feel, in more detail than you might expect). Lisa intentionally set it to up let her understand the people around her better, which has the side effect of Bitch recognizing that the girl who helped her out on one of her solo runs against Hookwolf's dog-fighting rings is suicidal, from being pretty much 'a puppy that's been kicked too many times, and is
still being kicked.'
Bitch being able to understand people better doesn't mean she likes talking, though, nor that she's any good at expressing herself, so she goes to Lisa for help. Of course, Lisa still has pretty strong issues with suicide, and especially with people
driving someone to suicide, but her ways of dealing with it won't be entirely the same (similar, very likely, but there would be differences for a number of reasons). Trying to find ways to attack the bullies in ways that making things better for Taylor instead of worse would very much be on the agenda, if they can get her to tell them (as this Lisa isn't Tattletale, the sort of bullshit deduction that canon-Lisa does either isn't happening, or needs more preparation, with different specialized 'divination tools;' on the other hand, she can do a lot more things, as long as she has time and material to work with).
I'll try to go into more detail about Lisa's power in another post, but a lot of what she makes are consumables, and/or grant Thinker powers or other relatively subtle effects. Not everything, though.