My question is since the former owner has no lease with the lot renters - there are 48 of them - would there be any legal problem with me having the renters sign a lease and increasing the rent immediately ?
probably. I'd check the laws in your state. In some states if you don't have a written lease, its understood to be a month to month lease. And the state probably has rules about notice to raise rents.
You need to take the time to learn your state landlord tenant regulations before you make any decisions. There is a lot of information you need to learn regarding the regulations governing your new business operations.Learn the codes before you risk ending up in court.