A water filter is not needed for Mount Rinjani. All clean drinking water is supplied by the trekking team, and the porters carry enough for the entire group for every day of the trek. Water is provided at meals, at rest stops, and before the summit push, so hikers never need to rely on natural sources or do their own filtration.
The lake and streams inside the caldera are not safe for drinking, but trekkers never need to worry about this because the team brings a full supply of bottled or purified water from the start. The only thing hikers need to carry is a reusable bottle or hydration bladder for easy access while walking.
Since the water is already handled by the porters, bringing a water filter adds unnecessary weight and is not required for any Rinjani route.