(And not relevant to your question, but no: even though LPL is not technically in the Whitney Zone, you DO need a Whitney Zone permit to spend the night there. You do not need one to day hike there.)
I based my previous answer on the many times I've looked down thru the trees at LP Lake from the main trail and seen tents there. Personally, I avoid LP Lake as it seems the mosquitoes are particularly bad there, but that may just be me.
Nearly all my trips up Whitney have been daytrips. However, on the 5 times I've done it as an overnight, the beginning date started the following day, and the ending date was two days beyond that.