Sorry if this question has already been answered, this thread is 44 pages long (!), it's too late at night for me to go hunting through all that, and I have yet to find the option in this forum to search within a thread, but I have the same problem with this joystick squeaking that a lot of others have, although nothing I've attempted so far has been able to fix it. I sprayed a bunch of dry silicone lubricant down into the works, tried rubbing lithium grease in there twice, in different places (yes, silicone and lithium lubricants are compatible, I checked), even took the whole thing apart and got into the mechanical area where everything functions, and sprayed a bunch of the silicone in there. The only thing I haven't tried so far is disassembling the whole sensor unit thing and lubricating each component in there separately.
It squeaks, yes, but that's not the main issue. The squeaking is caused by some minor sticking, which isn't really all that bad except for the fact that it will throw off my aim in delicate situations. It happens in the full range of the Y-axis, not just at the edges like is the issue with some others.