Under the hub cap is a castellated nut and split pin which hold the bearing race in place.
Remove the hub nut cap and clean out all the old grease, remove the split pin and throw away, remove the hub nut, washer and bearing and brake drum and rear bearing. Clean all the old grease off and feel for any play in the bearings and smoothness of rotation.
Repack bearings with fresh LM grease and replace the rear bearing, drum and front bearing, washer and hub nut.
Tighten the hub nut until you feel drag on the drum (Keep turning the drum as you tighten), then slacken off 1/4 turn and insert a NEW split pin to hold the hub nut.
HALF fill the hub nut cap with fresh LM grease and refit.
The drum should spin freely but not have any play either in the horizontal or vertical planes.