What is the ruling on exchanging gifts by lot among a group of people if the gift is of a previously agreed-upon value, and some of them did not adhere to that value? Is this considered usury (riba), and if so, how should the excess money be handled?

This action falls under the category of reciprocal transactions, and a gift intended for reward is considered a sale. A sale requires knowledge of the price and the item being sold. The ignorance of what each will receive through the lottery contains an element of gambling, so it is not permissible. Therefore, each person must reclaim their gift, and they should not revert to such an action.