When a lawn mower burns oil it's usually caused by engine oil getting into the carburetor or intake or exhaust system due to being tipped over.
Or if you haven't tipped the lawn mower over the oil could be getting past the piston rings and then getting into the combustion chamber where it's burned off with the gasoline.
If the engine has worn piston rings on the lawn mower engine then the oil can get past those piston rings and then get burnt.
If the piston rings are worn then you need to tear the engine apart to replace the rings which can be costly if you have a repair shop do it.
I once fixed a push mower engines piston rings and the piston rings cost $50.00 and then the seals cost around $20.00 and when I added the cost up it really wasn't worth the cost of repairing it.
But I wanted to repair it just for something to do and see if I could repair it so in that case the learning experience was worth it.
But if it's a push mower and it's burning oil I would just continue to add oil when needed and then scrap the lawn mower and buy a new one when it fully goes out.
I have an old push mower that goes through oil after every few mowing sessions and it's no big deal as it still runs okay and I had the push mower for 15 years now so if it went completely out I wouldn't worry about it and just get a new one.