Here's my experience with respect to a noisy hitch area when turning (which happens periodically). Assuming a properly lubed hitch head, I have noticed that the noise is created when the sway bars are not sitting completely flat on the L-brackets that are affixed to the frame. Assuming that they are sitting flat before beginning a trip, the L-brackets can/may move slightly when you go up or down a steep, short incline such as as driveway to a gas station. In that situation, the sway bars are applying a great deal of force to the L-brackets, and since the L-brackets are not bolted to the frame, they can move. You can verify if this is the case by looking at the bottom of the L-bracket (ie, where the sway bar sits) to see if you have equal or unequal scraping of metal across the L-bracket. (btw: you don't want to lube this area because it is what provides the friction to help reduce any sway) If you see that the sway bars are not moving across the majority of L-bracket (ie, by looking at your scraping pattern), then that is probably the cause of your noise during turns. If you re-adjust your L-brackets to match the angle of your sway bars, that will reduce, if not eliminate, the majority of your noise.
With respect to lube points, when I purchased my Equalizer hitch I also purchased a couple tubes of their lubricant (for convenience). I apply new lubricant to the ball before each trip (wipe off the old lube first, of course). I also apply a dab of lubricant to the top and bottom areas of the pivot areas and smooth in with a finger, but I only do this when the grease/lubricant starts to look dirty. This helps to ensure that the ball and pivot areas are clean and well lubed.
2004 Suburban 2500 LT 8.1L/4.10/4x4
Putnam XDR Class V, Equalizer 1400#
2006 Jayco Eagle 264BHS
Iota DLS-55, Progressive Industries EMS-HW30C, Trimetric TM-2025