I had a similar problem with one woman I dated. When we first dated, we agreed on nonmonogamy. She was staying with a guy and told me they were not having sex. I found it surprising, but figured she just wanted to "be friends" with the guy.
She was also seeing this other guy she was having sex with. So one day she says she wants to try monogamy with me so we could focus on making our relationship more serious. Once we worked out our problems with each other, we would open our relationship up again. So she went and told her other boyfriend that she wanted to be monogamous with me.
I found out much later that she had been having sex with her roomate. I also found out she had slept with her other boyfriend after we had agreed to monogamy. This was a huge warning sign. First of all because she lied in the first case when there would have been no repercussions. The second one bothered me because monogamy was her idea and yet she cheated.
It turned out that there was a long series of lies in our relationship. So I am very hesitant about accepting lies to "avoid hurting me." I think this is more extreme than in the case above. Yet after being burned on it, I am very sensitive to deceit.