Dave, straight shaft brushcutters have a pair of bevel gears in the housing at the end where the shaft meets the cutter head. The gears and their supporting bearings must be kept lubricated - the lubricant should be retained by the housing so you don't have to attend to it all that often. Each manufacturer probably has a specfic lubricant that they recommend, and of course that will be what they have used when they did their development and testing, so it probably works pretty well.
As far as I recall when I had a straight shaft machine (several years ago now) I used molybdenum disulphide automotive chassis grease - not a heavy grease, because the gears are running at 6,000 rpm. You do not need to fully pack the housing, it is better if it is about one third full. However if your particular housing has good O-ring seals on the two shafts, it may use oil instead of grease: oil is better than grease at high speeds, provided you can keep the oil clean and inside the housing. Looking in the owner manual is a good way to go - I didn't have that luxury since my brushcutter was an undocumented Italian one that I bought from a contractor when he decided it was too far gone.