Sounds good, I just sowed some and it all appeared in 4 days, with the seed tray on a shelf under my main greenhouse bench. So in warmth but out of direct sunlight.
I add vermiculite to the multipurpose compost when sowing lettuce, find its extra airiness helps seeds not to rot, lettuce does not like it too wet. Best moisten compost fully, then sow with no more compost on top, then keep in shade and don’t water until cotyledons visible.