Running out of gas while running should not harm your mower - I’ve done it plenty of times.
Could be any number of things:
Perhaps you flooded the line by over-choking after adding more gas? If choked too much, just let it sit for a while & try starting it again.
When was the last time you replaced the spark plug or cleaned the carb?
How old is the air-filter?
Lawn mowers are not too complicated, so there aren’t many things it could be.
Did you buy a used (likely repaired) mower?
If it’s quite old, there’s a good chance its time may simply be up.
Not saying for certain, but I suspect it is coincidental that the problem manifested after running out of gas.