There are three possibilities. The first is through a direct route. If you can imagine yourself having a couple of critters the size of dinner plates sucking the blood out of your body, you might imagine how there might be direct consequences of that through essentially physiological breakdown and death resulting. That's what probably happens to the very smallest fish.
The second is through diseases that might be vectored either by the sea lice—that is, transferred from farmed to wild fish by the sea lice themselves—or just through opening up lesions on the skin that allow diseases to get in, so the ultimate cause of death might actually be a secondary disease.
The third possibility is what I mentioned before: increased vulnerability to other mortality agents, such as predation and starvation.
Those would be the three routes.