Too much to go into here, but let me refer you to Harold McGee's less well known book, The Curious Cook: More Kitchen Science and Lore, where he has an entire chapter devoted to this topic, complete with tables for a whole bunch of fruits.
There's a few types of salsa -- salsa fresca (aka pico de gallo, aka salsa cruda), which is "fresh salsa" and uncooked, and if made fresh, it shouldn't be too watery (unless you add to much liquid, eg, lime juice), but letting the vegetables sit after salting will start to draw out extra liquid and could become watery.
For truly thick salsa, you have to treat it like a jam, and cook it to release the pectin in the tomato. (or I guess you could use some other thickeners ... I've never tried. tomato paste, maybe?) You don't necessarily have to cook the other ingredients, too, but I personally like roasting the peppers and onions to sweeten then up and remove some of the extra liquid. (halve the peppers and seed them, lay them on a tray cut side up with the onion cut into wedges, roast 'til they're softened, then dump into a food processor and either pulse or liquify it, depending on how chunky you like it. And the skin falls off the peppers, so I leave 'em out).
You can do the same roasting with the tomatoes, and it'll be thicker from the food processor, but you won't get the same cling without letting them cook slowly in liquid to develop the pectin. If you roast the tomatoes, I like to use plum tomatoes, as they have more "meat" to the gel around the seeds, and take out the gel and seeds.
Best Answer
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.