Lithium based grease is quite heavy. It is usually used for automobile moving parts where there is high friction (heavy load), fast moving parts & high temp.
the normal brown grease is suitable for 60dec C to 85decC temp & would be best suited for reels as it is lighter.
I did use the heavy lithium based grease, but realised while cranking the reel, although it is smooth the motion is restricted.
My dad always used singer sewing m/c oil
Regarding oiling, I use oil which came with my Philips electric razor.
...really fine, withstand high temp, non smelly, clear in colour & long lasting.
Here we use various types of grease for engines, pumps, motors, gensets etc & have a wide choice of stuff. Really helps when you are working with an engineering company.
I would definately be against the use of WD40 even to clean your reels. WD40 not only knocks of all the grease, oil and dirt, but creats a fine protective layer on the sprayed surface. WD40 has high penetration & could remain on ur reel for quite some time, even if you try to wipe it / wash it off.
If you apply oil /grease after using WD40, do you seriously think it is going to remain on the moving parts ? The effect would be something of a running nose.
A suggestion not as a specialist in reels, but from an engineering point of view. Just wipe the moving parts with a dry piece of cloth (do not use tissue) & regrease them.
Even metal has fine grooves & those grooves get deposited after sufficient wear of the gears (cutting in period). Thats why we have a running in period in automobiles (carbon deposit seals off all the pores / openings)