As you might have noticed already, displaying of lap times doesn't work anymore like it used to be.
Basically it has to with your best lap.

Observation example:
1. On your 1st lap you are setting a 1:03.376. It is displayed as such for ~1s, after crossing the line and is now your best lap.
2. In your 2nd lap you are driving a 1:01.111. It is faster and gets displayed like this.
3. In your 3rd lap you are driving a slow 1:05.465, but 0:00.111 is showing up. This means, you have been slower more than a second compared to your best lap.
4. In your 4th lap you are driving a slightly slower 1:01.756, but 1:01.111 is showing up. This means, you have been within the same second as your best time, but still slower.
3. In your 5th lap you are driving a faster 1:01.034. It is displayed as such and is now your best lap.

From this, you can judge during the race the following:
1. If a complete time shows up, you have been on your fastest lap or at least within the same second.
2. If it shows a 0:00.xxx, you have been slower than your current best.

Hope, that helps you a bit during longer cup races.