If you do time for shop lifing and the store got there stuff that was going to be stolen can the store sue you to

Shoplifting is a criminal act. They can't sue you, only prosecute you. They can sue for the value of the stolen items, but if they were recovered or reimbursed there is nothing to sue over.

If the store was out any costs, or if the items taken were not able to be resold as new by law or because of damage, they could sue you in addition to the criminal charges.