[GCV160 engine]
Lawnmower always stared 1-2 pulls until one day it won't fire at all, not even burp.
Okay, Honda GCV160 engine, what brand of lawnmower?
Does the mower have a manual throttle control?
Does the mower have a manual choke control?
If spark test is good, then short of some kind of internal failure, there is most likely a fuel/air delivery problem, i.e., too much or too little of either or both (air / fuel).
Using fresh fuel?
Choke operating properly (fully closed on cold engine)
New carb fitted with new gaskets...confirm they are all in the correct location, position and orientation. It is very easy to get one on backwards or upside down.
Ensure all rods, springs, and lever are correct when fitting new carb. There are multiple holes that springs can attach to, but only one is correct.
Be sure the two long bolts holding the carb, insulator, and air cleaner case are secure. It only take a small vacuum leak to make a "no-start" condition