They make speciality greases and oils for reels. tTpically each manufacturer has their own. I have tube of Penn grease that has been around for a long time.
Grease such as WP bearing grease could be too thick when it is cold outside, too thin when it is hot outside, and may not have the properties for good corrosion resistance, as well as lubricate adequately cause it does notflow well. Being too thick could make the reel handle hard to turn, the bail to not trip adequately etc.
There are newer more modern greases and oils specifully made for lubricating reels also. Check Bass Pro, Cabelas, etc. for mail order sources.