The 2MT taper just locks in because it is a shallow taper. Similarly the chuck locks onto the arbor because it also is a shallow taper.
In the case of the chuck to arbor taper you don't want this to ever come off so don't use anything to lubricate when it is assembled. Just perfectly clean and a good rap on the end of the MT taper with a plastic hammer to drive the JT taper home in the chuck is all that is needed. Althougn I have to admit I once cinched one together a tiny bit in a big vise.
You do want to be able to remove the MT taper from the tailstock so a bit of light mineral oil is a good idea here and a gentle rap with the plastic hammer.
Before inserting the MT taper you should, however, crank the tailstock forward a few turns on the handwheel. The tailstock should have a protrusion on the end of the screw that will push the MT taper out when it is fully retracted.