I think possibly so. It's my understanding that spousal support is often subject to termination or reduction if the receiving party cohabits -- that is designed to prevent them from "cheating" on the remarriage rules by simply not getting married. I would not be surprised to find the courts applying this principle regardless of the gender(s) of the parties involved in the relationship.

If she has a live-in lover, that implies possible extra income, and you should talk to your lawyer about it.