I've looked all over Google for a stopwatch app that records laps (which they all do) but also records a time of day timestamp. If it can't do the example below, at least record the initial start time of day (and I can figure out the rest).
Start (10:09:00 am - I want to know I started at this time)
Lap 1 - 00:01:02 (10:10:02 am)
Lap 2 - 00:12:12 (10:22:14 am)