1.8 ohm draw with the car parked and turne off would imply over a 6 amp drain on the battery with the car turned off. That’s more than 60 watts. I can’t imagine anything drawing that amount of power when the car is parked and turned off. Some cars leave the lights on for a while after you park the car now-a-days, so that might be what you are measuring. Maybe someone here knows how to disable that “feature”. If the ‘temporary lights on’ is not the cause, then something else is wrong with the car’s electrical system; that’s what is draining the battery. First thing I’d do is carefully inspect the wiring harnesses connecting directly to the battery. Are there any frayed wires? Is the positive terminal of the battery close to any chassis component, bolt, etc, which could be grounding it out? Is the battery loose at all? Can you move it around? It should be solidly in place so it doesn’t jostle around when you are driving.
It’s true as Tester says, a battery can fail suddenly, but from what is said in the OP, I don’t think that is the problem in this case. If it isn’t an obviously observed short in the wiring harness, the first thing I’d do is completely disconnect the alarm system. Especially if it aftermarket. The technicians who install these things sometimes take shortcuts.