Hi, The appraiser should only make a recommendation and the bank should be the one asking since they are funding the loan. It depends on the type of loan you are getting, some may have strict rules on possible lead based paint issues. Peeling paint is one of the ways the paint can cause harm (if ingested, etc).
That sounds like an unconventional request from an appraiser. Typically, appraiser are hired to contribute an opinion on the probable market value of a property. That should be all. Only an inspector would make recommendations for certain repairs to be completed, sometimes to meet regulatory requirements and other times for aesthetic or functional reasons.