From what I've heard, she dies every time if you dump her in ME3. Not so if you dump her in ME2. I automatically assumed you dumped her in third game, but I guess you did that in second?
My bad.
She definitively can live even if you haven't broken with her in ME2. The key point is to not explicitly break with her in ME3. So here's the process:
- first meeting : you tell her that she is still important for you (so you keep the possibility to continue the relationship);
- second meeting (with her hologram) : nothing special to do, I think that choosing the parangon options is enough ;
- third meeting : you say that you trust her and give her access to the Alliance's ressources.
With these three conditions, she survives even if you engage a relationship with Liara before the third meeting.