I am an Equalizer fan and have had two over the last 16 years or so. I lube mine up and use white lithium grease on the head AND on the L brackets. I only put a "small" amount of grease on the head and even less on the L brackets.
As previously pointed out, the main anti sway resistance comes from the head and yet Equalizer says it is OK to grease these surfaces! They say that applying grease to the L brackets "is not recommended." If this was a bad idea, why wouldn't they say "Do NOT grease the L brackets"? I figure adding the pads is not a lot different from putting a skim coat of grease on them.
I am speaking from my experience. My hitch is pretty quiet and has been all of the years I have used it. It always confuses me when people post that they got rid of their Equalizer because they couldn't stand all the noise. You don't have to put up with the noise if you don't want to.