Running it out of fuel wont have caused the carby to gunk up, but something is making it run lean, it could well be worth dropping the float bowl off the bottom of the carby and taking a look inside, its unlikely to have much if any dirt inside unless the strainer in the tank has become damaged.
The gcv160 motor is quite a fussy beast, they do not like fuel that isnt 100% fresh, I had one coming in regularly with stale fuel, it was after the third time I tipped out and replenished the fuel its owners decided to throw away their $5 in fuel in the old can and get fresh stuff.
Also if they get any water in the fuel system, they can behave very irratically, such water will be seen in the fuel bowl when removed along with any dirt that may have built up, if there is evidence of either, it would be a good idea to clean the jet out.
