When I think of lap times, I think of the total time it took to complete a full lap.  That would include any stopped or "paused" time.  That is the same way segments are measured, so people can't stop mid-way for a rest to try to get a faster time.  If you look at any race or event, they don't stop the clock when someone takes a break part way through, the calculate the lap times based on the finish time of day minus the start time of day.

Hi @donpwinston this is working as intended. The moving time feature on Strava is used for all activities that don't depend on fair competition (races and segments). Competitive features such as laps, segments, and activities tagged as a race use elapsed time. Moving time is the time you were in motion and
elapsed time is the total time from start to finish of the activity.

If you want to take some breaks between laps, this time will be included even if you paused your device.

You could start a new lap for the rest so that it’s contained in its own lap.

Note: If you are looking at analysis > laps > the average speed shown on the analysis graph is using moving time. If you look at the laps view, it shows laps using elapsed time. 

You can read more about Moving Time, Speed, and Pace Calculations in this support article.

I would like it too when laps use only the moving time for the average speed so I don't have to press the lap button before and after every traffic light or other impediments. Laps are created by myself for myself in my individual ride so there is not the slightest possibility for competition here.