Hi. Had a look but couldn’t see this addressed elsewhere.I believe there may be a bug in the leaderboards.
If you set a next fastest time on the next lap, then that should show when the first one expires. I believe this isn’t happening.
Also sometimes it seems to me that if you set a faster time than one you have already set, it may not show. I suspect this could be happening when your position on the leaderboard would not be changed by the new time. eg still 10th.
Combine the 2 events and you can set a fastest time that never displays.