i am supposed to go hunting on lake lavon this upcoming weekend and realized that the only firearm they allow is a shotgun, nothing larger than #2 shot, would that be effective in taking down a hog?

With the right Shot placement it should.

What do you think the max range of effectiveness is?

30-40 yards if a 12 gauge, 20-30 if a 20 gauge.
Just don't try a big pig and aim for the head.

Areas 6-13 you can use smooth bore shotgun with rifled slugs.

Authorized Weapons

Hunting the legal game noted below is permitted in designated hunting areas only. In areas 6-13 feral hogs may be hunted with Smooth Bore Shotguns (slug only), in all other areasFeral hogs: bow and crossbow only. 

thanks for the clarification i misread the information on the website i appreciate it zoeDoog

Yes sir, welcome. Good luck out there.

have you had any success on lake lavon?

Yeah, but you have to be willing to put in the miles. There's allot of feeders on adjacent land on the north side of the lake and some good areas that have good oak and pecan tracts. Good trails aren't too hard to find. Thermal definitely helps to find them from a good distance.

A few from last year.

Are those from Lavon??

One on the far right is the other two are from Coffee Mill.

I hunt on the south end of Lavon but it is only for eradication for a corn farmer. 2015 was slow being that I only killed 73, the 4 years before that I'd average about 180 a year. Biggest being 260lbs