Whether or not it's worth the cost to repair a lawn mower depends on the amount of repairs the lawn mower needs and the cost of those repairs and whether you do the repairs yourself or hire out the repairs.
Sometimes the cost of repairs can cost as much or near as much as a new mower especially a push lawn mower.
If you take a push lawn mower in for major repairs the cost could be around $100.00 or $150.00 which is near the cost or as much as a new push lawn mower would cost.
Simple repairs such as a pull start rope or cleaning the carburetor would be worth it to me on a push lawn mower but if the engine needed to be replaced or rebuilt then the push lawn mower would just go into the junk pile.
Now if I needed to replace the engine on an expensive riding mower such as a zero turn riding mower that cost me over $1,000.00 then buying a new engine or rebuilding the engine or other parts on the lawn mower would be worth it if the lawn mower is 15 years old or younger.