I have about 20 auction lots I would like to get rid of.....(things that didn't sell and I donated or maybe a relative wanted it) but I'm pretty sure I shouldn't just delete them or I might lose some pictures connected to other auctions. Should I just do a purge and archive?
That depends on how the auction lots are created.. If you are using Inventory items, then the Auction lots can be deleted without impacting other images on other lots.
If you delete, run a backup, then rebuild to make sure the database is in order
You can also choose to archive the records away if you want. Or you could manually mark as Sold/shipped. IF you do that be sure to go to the Inventory item and make sure the qty in stock and qty available is accurate.