How do I make my sorbet thicker?
The problem could be the recipe. If you're using a lot of lemon juice, then a lot of sugar to cover up all that acidity, you're guaranteed to end up with something pretty soft. Have a look around at other lemon sorbet recipes, and see if you're using relatively more.

But if your recipe is sane, then it could be your process. Here's how it could mess things up. 

Sorbet is basically sugar water with a bit of flavor. When it freezes all the way, unless it was churned as it froze, there's going to be a tendency for it to separate into ice crystals and even stronger sugar water. Some of this may happen in your first freezing step. Then you're pulverizing it in a food processor, probably giving it a chance to melt a bit. This is much worse than just leaving it out, since once it's in tiny bits, there's a lot more surface area exposed to air, and you're continuously mixing it, bringing in warm air, and so on. Then finally, it refreezes. The part that managed to melt in the meantime is going to repeat the earlier process, except now there's lots of space, so it's even easier for ice crystals to form and force out the sugar. So I'd definitely expect a tendency to end up with a runny sugar syrup component to your "sorbet". (If it's at all grainy, this is probably what's happening.)

If you're determined to do this without any kind of ice cream maker, it's going to be hard to avoid problems. You can certainly try to correct for it by using less sugar, though. You could also just make a granita - freeze it on a sheet, and scrape it off to serve.