It is better to repair a lawnmower if the cost to repair the lawnmower doesn't exceed or is less than the cost of a new lawnmower.
If the cost to repair the mower costs more than a new lawnmower or even the same or close to the same as a new lawnmower then it's better to replace the lawnmower.
Most push mowers should last 5 to 7 years if maintained properly although some push mowers may only last a few years if not maintained properly.
Most riding mowers should last between 10 years to even 15 years and sometimes longer depending on the quality of the riding mower and how well maintained it is.
As long as you change the oil, keep the lawnmower clean, replace or sharpen blades, replace belts when needed etc the lawnmower should last a long time.
When the lawnmower is getting past 10 years old and is a riding mower especially of the cheaper quality then it may not be worth it to keep repairing it unless it's just small things but even something like replacing the deck belt, deck pulleys and even the deck spindles can be worth it if the engine is in good shape and the mower itself is in good shape.
You can buy a lot of mower parts cheaper online and repair the mower yourself if you know how.
But if you have to hire a repair shop then the labor cost can add up and not be worth the repair of the mower unless it's a very expensive mower such as in the $5,000.00 range or more.
Also when storing the riding mower or push mower be sure to run the gas tank out of gasoline and the carburetor as well.
Gasoline that is left in the carburetor will gum up and clog the carburetor and lead to failure of the engine to start until you clean out the carburetor or replace it and the old gasoline can also turn to varnish in the gas tank.
I always run my mowers out of gasoline before storing and then on my riding mower I shut a fuel shut off valve off and let the engine run until it dies out from no gas which means the carburetor is clear of any gasoline.