I very much doubt they would have gone for Lewinsky as the case at the time. A presidential affair in and of itself would be very difficult to turn into something impeacheable. That's not to say that there weren't those who voiced the concern at the time that Clinton was a sexual predator who abused his power to get young women to sleep with him under very creepy pretexts, but those were very much in the minority. Indeed, pretty much all leading feminist voices at the time (Betty Friedan, Gloria Steinem, etc.) not just firmly supported the President, but were outright hostile to Lewinsky. It is first in a post-MeToo era that we've begun to see some re-evaluation on the matter not just about how Bill Clinton actually behaved, but how he consistently surrounded himself with people to whom Loyalty to the President was the only virtue there was in the world, and so were very keen to cover up his tracks and protect him.
Newt Gingrich impeaching Clinton over being a problematic sex pest, however, I find even more difficult to see.
In all likelihood, the impeachment would have been over Whitewater.