Contact cleaner is not a lubricant, it's intent is mainly as a solvent for first cleaning and flushing out old dirt including stale grease.
These analog joysticks need to be cleaned, they get food, dust, hair etc. inside the gimbal mechanism, and the factory grease dries out.
You can use a q-tip wetted with IPA. Then a light grease is used for the mech and PPE like Faderlube for the potentiometers.
I've replaced a bunch of analog joysticks on Xbox, they use (turquoise) Alps parts and there are cheap Alps knockoffs from china as well. The pots do wear out. Very difficult to desolder.
Best is a little space lubricant with teflon, I tried that and the guy started winning so good it caused a family uproar lol, the gaming expert was no longer that. It was on the front fire buttons I put Krytox 105 oil, there is also Krytox grease I have not tried out.