A loose doorknob of any kind is a nuisance, and if left unfixed, it will eventually fall completely off the door. When dealing with a lever door handle, fixing the problem will require only the most basic of tools and about 10 minutes of time. Levers handles slide onto a rod assembly with a set screw. This screw fits in a groove on the round lever rod. A loose lever requires some readjustment to properly fit into the rod assembly.
Determine whether you will need an Allen wrench or a screwdriver based on the style of set screw, which you will find on the bottom of the door lever. Remove the screw, and slip the lever handle off the rod.
Inspect the rod's surface, and locate the groove where the set screw needs to be secured. Replace the handle, aligning the set screw hole with the groove.
Reinsert the set screw and tighten firmly with the Allen wrench or the screwdriver.
Repeat this process on the opposite side of the door lever to insure a tight lever door handle.
Take care when dealing with set screws as they are small and can easily be stripped.
If set screw is stripped, bring it to a hardware store to use as a template to replace the screw.