How to repair a lose door handle?
If you are handy at doing things and can see how things go together, it can be fixed, I believe without a locksmith.

There should be a set screw on the lever that can be tightened. The picture you have does not show that side of the lever, but if it did you may find it to be an allen (hex) set screw. 

In some handle sets, the allen screw has a very long sharp point to dig into a specific spot on the shaft. Sometimes the shaft is not set in the proper orientation for that to happen and the handle gets loose not matter what is done

If there is no allen set screw, the handle is kept in place by circlips


on the back side (inside) of the interior backing plate. Remove the 4 screws, the backing plate will come off, you my find some loose parts in there still around the shaft, unless they are broken