Think you can technically leave LAX at 6 or 7am, and get a return flight around 8pm, but if your heading back to LAS, there will an overnight somewhere.
Did look at LAS-LAX-JFK return. Bit more time needed and a few £ hundred more (£2.3k for 500TP), but can be done.
If you specifically book Flagship / a transcon (from LAX, SFO or maybe SNA?), you should get flat beds.

Suppose you could catch one of the 10pm or so flights overnight it to JFK and then easily get back next day.

Remember, west coast to east coast has a 3hr time difference on top of the 4-6hr flights.

Pretty much anything other than the transcon will be a recliner seat.
Think you'll need 1-2 days to be honest. LAS isn't always the cheapest starting point either.