As I suggested a silicon based spray grease or even one that PTFE in there as well, WD-40 I think has a variant that satisfies these requirements.
Edit:- from my way of thinking, once a metal shaft and nylon bush have started to makes these noises, similarly the end of a push rod against a nylon cup or nylon/plastic switch plunger against a steel pedal, then there will be permanent damage ie marking/scoring so all you can do is minimise this getting worse and off course quieten it down.
My 2011 Audi S4 clutch pedal starting making noises while it was still under warranty, so it was handed in and all likely points sprayed with a suitable lubricant, and even now 6 years on it is still okay, so spraying slightly damaged areas can work, I was surprised by that, I thought that I'd be knocking on their door again within a few months!