Anytime someone does something like the the comments made by Trent Lott, it embarrasses not only the individual,but the party itself. No one wants to be associated with a person like that in the public eye, whether they like and agree with them or otherwise. It's just the way it is.
No, his choice to resign was all his. He could have easily stayed and kept fighting for votes. If you look at the mayor of Toronto, he was asked to resign but he said no, and he was in trouble for something way more serious, since he was doing drugs.
I believe Trent Lott's decision to resign had to do with the Honest Leadership and Open Government Act and Lott's interest in being a lobbyist over a politician. I believe the fact that he opened a lobbying firm directly after is proof of that since the incoming legislation would have made him wait longer. I do not believe his comments at Strom Thurmond's birthday party were the main reason.
Many people think that the comments made at Strom Thurmond's party was the only reason that Trent Lott was forced to resign. By analyzing his recent voting history, an analyst can see that he was already not on friendly terms with the party. The party was arranged prior to that, and it would look petty to uninvite him. So he was allowed to attend and speak, but he saw the writing on the wall and was just taking a final chance in public to address some issues.
No, Trent Lott was not forced to resign by his own party after his comments at Strom Thurmond's birthday party, because most politicians can put their foot in their mouth without their being any serious consequences. There would have been no serious consequence for Lott if he had decided to keep his position.