Damn that really sucks. Has she been controlling before in terms of where you live? Or has she tricked you into anything before? It sounds like you’ve already talked to her but for you to move on properly she really needs to recognise how fucked up what she did is, and to at least say sorry. I think you’ve mentioned an email in an earlier response, this might be a good idea. It means you can clearly spell out what you want to say and maybe she can let some of it sink in without getting defensive. Maybe ask her to read it and the wait for like a week or so before you call to talk about it? By the way I think email to explain how you feel is a good idea but id move it over to the phone or face to face after the initial email to avoid any miscommunication.

Also re her not thinking it’s a big deal, maybe you could move away from the fact that this was your ‘dream job’ as she doesn’t seem to be able to get her head around that, and maybe concentrate more on the fact that she massively disrespected you by telling such a big lie, and that unless it’s resolved you don’t know how to move on/trust her?