Broken lever and lock

We ordered your part # 82-107 : Sliding Door Latch Lever Kit thinking that was all we had to replace, but then realized that the "bar" (not sure what it's proper name is) that slides into the lever and the key cylinder looks to be cracked and that is what actually may need to be replaced. But I can't find something similar to what we have on your site. Can you identify this part?

So, we watching the video showing how to replace the lock set and thought we may actually have everything we need. But now we find the real trouble may actually be the lever. It does not stay in place. It seems there's nothing holding it to the door handle. We get everything installed and flip the lever and then it falls off. Is there something missing?

Watching the video of you installing 82-073 it looks like the lever should be securely attached to the handle. Ours isn't and just keeps popping off.

Thanks