Compound Hunting Bows are unique in that they use the mechanical advantage of pulleys to reduce the hold strength versus a conventional recurve Bow we all grew up with.
Point being these pulleys run on bearings that need to be lubricated and done so without over lubricating, keeping the lube where you put it and not to give off any odor that Deer and such can smell from a long way, or as you get closer to that Boar you have been stalking for hours.
Items you want to try here are the Gun Snot Liquid Lube as it is very thick and has minimal migration. the expression 'Dots not Lots' definitely applies here. Point being Gun Snot is a highly effective lube so you do not need a lot. the other item that you want to look at is the Gun Snot Gold. Versus the liquid, the Gold has some Teflon in it to make a very thin paste.
As usual, use brake cleaner (red can) to prep the pulleys so you get the old grease out of there that might have polymerized or is just a dirt magnet. Then apply either the Liquid or the Gold. Do a few pulls and see where your dots are working and add or wipe off excess as needed through trial and error. Less is more.
So prep the pulleys before using with the Liquid or the Gun Snot Gold that is thinner than Conventional Gun Snot Paste. The key words here are "Dots not Lots". Apply the lubes as dots on the pulleys, but not Lots of lube - you do not need a lot to be effective in lubing a pulley. It will smooth it out as you use it. If the Gold is too thick for you - you can thin it out with the liquid.
Lastly the "thickness" of the lube changes minimally over a wide range of temperatures. There are others that claim this, but you can prove it in use - when seconds count, Gun Snot will perform the same in Arizona as it will in Fairbanks.