ex-wife asking my boyfriend for lunch..calling her self Mrs. (his last name).

I certainly don't know for certain but I don't believe that's possible, is it, ehBeth? Bigamy requires a second legal marriage when a person is still in another.

It depends on the jurisdiction.

In the jurisdiction I work in, 3 years living common-law, or 1 year living common-law and having a child are two of the circumstances that turn a common-law relationship into a legal marriage.

If there is another documented marriage - kabooom - bigamy.