Greetings:
Actually, that lip is what you use for gauging the tire if your wheel center isn't crooked or wobbles as Kelly pointed out. Also as Kelly pointed out, the wheels ought to be trued on their OD and outer edge for the tire to run true. When purchasing new tires, the wheels should be turned round on a lathe and the outer edges turned square with a little chamfer at the outer corner so as not to foul the little radius on the inside corner of the tire (don't ask me how I know this!)
Also, you shouldn't have to beat the tire onto the wheel. As Kelly says, when the tire is heated up to 400 degrees Fahrenheit it will expand enough to slide easily over the wheel.
Then, with at least three large, heavy "C" clamps (with set screws) that you have made to fit over the tire and long enough to fit down over the wheel so you can clamp the tire to the wheel, tighten up the clamps quickly, yet evenly, which will draw the lip on the tire up against the wheel. Now you'll have to wait until the tire cools before removing the clamp.
Or, you can install the tires with the wheel vertical and lower the tire onto it. I've also seen the wheel set lifted and placed onto a heated tire laying on several bricks on the shop floor.
I have been in shops where after the tire is set and cooling the tire is struck with a ball peen hammer several times. I suppose that is to make sure it is seated or maybe it is just for good luck...
And good luck to you!
J.David