https://www.bradington-young.com/ryder-liftrecliner-chair/8010-816/iteminformation.aspx

This looks a bit more streamlined than the puffy recliners you mentioned. I would suggest looking at your local stores to see if there is anything in stock. Custom orders are taking months to complete.
We recently purchased a leather Lazy Boy recliner for my dad. Fortunately they had the first one he sat in available, and we were able to take it home that day. Since then, I have heard/read about horror stories regarding quality issues with their furniture and orders taking many months to complete. (We are also shopping for a new recliner for my 6’4” husband!) We found some nice recliners at a Flex Steel dealer.

This one is from Home Depot. Looks pretty nice! https://www.homedepot.com/pep/ProLounger-Power-Recline-and-Lift-Chair-in-Caribbean-Blue-Plush-Low-Pile-Velour-RCL78-CNF55-LT/309978196?source=shoppingads&locale=en-US&mtc=Shopping-BA-F_HDH-G-D59-59_34_INTERIOR_FURNITURE-MULTI-NA-Feed-PLA-NA-NA-059_034_003_LIVING_ROOM_FURNITURE_Living_Room&cm_mmc=Shopping-BA-F_HDH-G-D59-59_34_INTERIOR_FURNITURE-MULTI-NA-Feed-PLA-NA-NA-059_034_003_LIVING_ROOM_FURNITURE_Living_Room-71700000045547815-58700004666510332-92700061190213156&gclid=CjwKCAjwzMeFBhBwEiwAzwS8zLf4MemIKJFukFvDacrqOVPMTMMrkW8RBdjSedPgaOszjMhmAnacsRoCdzcQAvD_BwE&gclsrc=aw.ds

https://www.overstock.com/Home-Garden/Furniture/Lift-Chairs,Modern-_and-Contemporary,/chair-type,style,/32/dept.html

Lift chairs are DME (durable medical equipment) so check local medical supply stores too. Your father's PCP can write a prescription for it and Medicare (certain parts) will pay part of the cost if purchased from a Medicare-approved supplier and there is a documented certificate of medical need. If possible, have your father try the chairs and also work the controls to make sure he can use them (sometimes simpler is better).

I should have specified we are looking for leather, and dad is about 6’ tall.