Canned beans certainly aren't ideal but they're much better than pre-ground. Even Illy preground isn't really fine enough for a lever machine and that's a finer grind than Lavazza.
There's no doubt that you will get better results with freshly roasted beans, but I wouldn't rule out the grinder or grind setting either, or something else. Any chance of taking a picture of some of the ground coffee on a sheet of white paper? That might help. You can also try pinching/rubbing some between your fingers. It should feel almost like flour, but still gritty. Is the grinder clean? Is the machine clean inside behind the screen?
What I'm finding difficult is your description of the coffee tasting sour rather than bitter sbenyo....
All that said, you have already seen that simply changing the beans results in a big improvement, so I would persist in trying to find some freshly roasted beans and work on your technique in the meantime. I'm sure someone in Israel must roast fresh and deliver by post at the very least. That's how I get hold of some truly wonderful stuff over here.
So for the time being, I'd just change one variable at a time....
Anyway, I wouldn't recommend canned beans to anyone over the "real thing", but still feel (actually know) that this coffee should be looking better than it is, even if one is grinding Illy canned beans - unless it's a can from the sixties.....
I've used a Pav to make coffee using Illy preground, for goodness sake, and it sill looked and tasted passable....
The coffee in the UK is generally garbage, notwithstanding a few stars in the firmament. There's a decent roaster in Brighton, but the coffee served in their bar isn't brilliant. There's one Italian restaurant that know exactly what they're doing, thank goodness, and a little chap with a delicatessen who makes something drinkable. Otherwise there are now plenty of places with nice equipment but either bad beans or bad technique or generally both. So it's not tough to do better.....
Cheers
Mike
LMWDP No. 237