This is just like an automobile brake and would be fixed using the same techniques.
First make sure the lever is moving freely, and is not "bottoming out" due to the cable being too tight. (To adjust the brake you do not tighten the cable but rather adjust the eccentric that is opposite the lever pivot. Then adjust the cable to match.)
Lubricate the pivot lightly, but do not get any lubricant on the drum or shoes. If need be, wash off any oil or grease on the drum/shoes and wipe with a naptha-moistened cloth, then sand the shoes lightly to remove any glaze.
Examine the shoes to make sure they are not worn out, and examine the drum for serious scoring.