If person was married in europe, lied on naturalization papers that was divorced but actually never was, remarries in US(stating on marriage license was never married before); divorces 2nd husband, then remarries 3rd husband,now seeks divorce and lots of $$ from 3rd husband. 3rd husband now finds out she never divorced first husband, can his marriage be annulled and is she entitled to $$ or must he proceed with divorce? He was married in NY. Secondly, is it criminal for her to lie on naturalization application regarding marital status and would anyone care?

Yes, of course, husband #3 can seek a nullity (or "annulment" in many places). Bigamy is always grounds to annul a marriage and wife would not be entitled to any portion of the property husband generated during the marriage if the grounds for nullity were proved. Nor would she be entitled to spousal support ("alimony") or attorney fees.

Yes, and it is criminal to make false statements on an application for naturalization.