Question on Singapore airport hotel

Wife and I are flying to and from SIN on Delta this Aug. On outbound leg we will be renting a car in SIN. I'd much rather crash at the airport hotel and clear customs and pick up the car after a few hours sleep. I've heard that on connections without luggage transfer people have just allowed their luggage to go to some sort of "left luggage" place and picked it up after their airport hotel stay. Can you do this if your "connection" is with ground transportation?

And a similar question, on the return. Is this a viable thing to do between a LCC (probably Lion Air) flight to SIN in the evening and before the 6:00 AM Delta flight out?

Thanks