Since only one score for person is kept, you wouldn't be able to do this retroactively. Example:
Player A has 20 set on May 1
Player B has 20 set on May 1
Player C has 21 set on April 30
You can't conclude that Player C used to have a #1 for this room. It's possible that Player B scored 21 on April 29 and then improved her score when she was beaten. A My Lost #1s page would only be able to keep track of those #1s lost after the page was implemented.
An idea that I've been meaning to suggest is to change the way the scores on the My Scores page are ordered. Currently they're ordered by date the demo was recordered. Suppose this were changed so that they were ordered by the time that they achieved a given rank. Then whenever you lost a #1, you could go to your My Scores page and check out your #2s; any recently demoted scores would be at the top of the list.