One of the things that cause the mower to run poorer, start harder, and finally stop is a plugged air filter.  I've seen this a lot, maybe 20% of dead mowers - especially the classic Briggs and Stratton engines as shown:

Out of sight, out of mind.  The mower looks nice and clean, but look at this mess, the engine is trying to inhale air through this!

The foam comes right out.  This is plugged.

So what I do is fill a coffee can with hot water and a little diswashing soap.  Clean off the foam, wring it out, and put just a little motor oil (or the official filter stuff) on the foam.  Wring it out again and reassemble.

Ought to look like this, it will probably run now.
HOWEVER, if the filter was plugged up like that it has probably fouled the sparkplug (which will also need cleaning) and in some cases will even start sucking the oil out of the crankcase!

Here's an impressively plugged side flow air filter

Here's the all time record for plugged air filters!