In Formula 1, the fastest lap is the quickest lap run during a race. To set the Lap Record, the lap must be the fastest lap recorded under race conditions.
In other sports you would have qualifying rounds, and records can be set in those rounds because those rounds are similar to the final event conditions complete with other competitors.
Qualifying is counted as a practice session, it is not under the same conditions as a race. It is a totally different "game" to the race. You go out there in your own time, sometimes with "qualifying engines" or "qualifying fuel" and tyres to set the fastest lap time. The game is not the same as the race, which is to legally cross the finish line first, so those times cannot be compared with race laps.
With that said, would the proposed "Sprint Qualifying" fastest laps qualify to be Lap Records? I would think, yes.
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Online Stress Therapy. #77 is mediocre. W12 is the fastest car. Repeat x 1,000