here's the thing-- lying is NOT a symptom of DID at all. Appearing to lie (claiming to be the opposite gender, a child, an octogenarian, etc.) is pretty common, but pathologically lying isn't.
However, having DID, I can speak from personal experience and tell you that I have a couple of alters who are horrible liars. A couple cry for attention (that's only half-'fake', I guess), and at least one or two in our system will outright lie about things. I think it's more to do with the mental illnesses that we have, the ones that are apparently very co-morbid with DID-- BPD, especially, but then the anxiety and depression don't help either.
I'm not a doctor and especially wouldn't try diagnosing your gf/ex-fiance/whatever over the internet, but her behavior sounds... confusing. It might be DID, or she might be a pathological liar and/or have borderline personality disorder and/or has bipolar and was misdiagnoed, either at her conscious 'helping' or just because they didn't know what else to call it (It wasn't seen as commonly 20 years ago, though). I have no earthly clue. But people with DID don't generally split a new alter everytime they run from someone... and especially not if they've been diagnosed for 20 years. I definitely think there's some other issue tied into the DID, though, because that kind of lying really isn't typical in a dissociater... or maybe she's not lying, just confused? You never know. I honestly think that if she does have DID, some of her alters MUST have another mental illness, if her entire system doesn't share it. Going to a psychiatrist would be a good idea, but I'm afraid I don't know a good one.
As far as where to go from here, you have to explain to her that while you love/like her and want to be with her, you have boundaries that everyone in her system needs to respect. Remind her that you're supposed to be a team, the two of you against the world, and that for it to work she can't lie to you.
Check out
The Significant Other's Manual to Living with DID... My partner and I have found it to be the funniest AND most helpful guide out there. Sounds like you've got your hands full. Best of luck.