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.
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.