How to transfer tax withheld on S-Corp income to shareholders?

For Federal, it's almost certainly backup withholding, and I enter it as backup withholding, which gets passed through on the K-1 without issue. Also they should make sure they give the division order folks sufficient information soon enough that they aren't subject to backup withholding next time.

For the states, every state has a different process for nonresident withholding, and the Lacerte input tends to be in wildly different places for each state. If you tell me which states you've got, I probably know or can figure out where to enter the withholding.

If you don't do a lot of multi-state oil & gas, be aware that there's often but not always a different apportionment / allocation method available for oil & gas activity. 

Also watch out for states that have different permissible depletion rules. If you use Lacerte's oil & gas input screens, it should work just fine for royalties. (Working interests work, too, if you have all the info and key them individually and aren't bothered by dollar rounding. But an aggregate entry with limited info is likely to arrive at the wrong answer for working interests and a reasonably right answer for royalties.)