I need to submit an amended 1120-S for my S corp. The Schedule K isn't affected by the amendment. Will the IRS require me to submit a revised K-1 to my lone shareholder?

what are you amending that doesn't affect schedule K? it may be that an amended return is not required.

Estimated taxes paid were not required. S Corp is due a refund. Don't believe that impacts the schedule K. Is an amended return required?

How did you even pay estimates for an S-corp ?   Normally they are made personally using the SS# of the owner  and not the company's EIN.  

If that is all that changed on the 1120S then it would not affect the K-1 so no amended K-1 form needs to be issued.