Say I have a 3U cubesat with a BIT-3 ion thruster, an iodine tank and landing legs. Can it land on the Moon with just an ion thruster?
Not a soft landing.
A soft landing requires the spacecraft having a thrust-to-weight ratio greater than one (otherwise it just falls faster and faster).
Ion engines have a very low thrust to weight ratio, much smaller than one. On the moon, the surface acceleration is 1.625m/s², so the thruster must provide at least 1.625N of force for every kg of spacecraft. Ion engines are several kilograms, while providing less than 1N of thrust, so this is not possible.
- Mass: 1.28kg without gimbal.
- Thrust: up to 0.00125N
- Thrust to weight ratio on the Moon: 0.0006 (best case, assuming the spacecraft is 100% engine by mass)
Just smashing into the surface of the moon at more than a km/s on the other hand does not require slowing down.
Not with an ion engine.
There is nothing fundamentally impossible about putting an engine in a cubesat and making it into a lunar lander. However, this is a very difficult feat, nobody has done anything like it -- cubesats with any significant engines are still uncommon though they do exist.
It should be noted that rocket fuel or high-pressure gas will make launch providers significantly less willing to launch your cubesat.
But any engine describable as an "ion engine" is totally unsuitable for landing on the Moon with anything like current or plausible future technology, and it only gets worse if it's a cubesat.
First, ion engines in general have miniscule amounts of thrust for their weight -- as little as 0.00125 N of thrust for an engine that weighs 1.25 kg (12.26 N) just for the engine as stated in the other answer. You need to be able to hover to land softly, and you need to be able to come at least close to hovering if you want to land hard-but-less-hard-than-smashing-at-orbital-speed.
Second, for an ion engine you need an external power source, and power sources are heavy -- and the amount of power needed goes up rapidly with trying to increase the thrust. And many power sources are not readily able to fit into a cubesat.
You're better off using hypergol.