If the lever is causing the rattle, just remove the stock from the rifle by pulling the stock to the rear, and instead of pushing up on the lever, pull down and pull the stock off. (use the video that Japes posted for more detail instruction)
Once the stock is removed, there is a roll pin in the plunger that holds the the lever in place. Remove that roll pin and you can tighten the nut down a few threads on the plunger. Just make sure to leave it where you can re-insert the roll pin. This increases the tension on the lever where it doesn't move around as much. I fixed one of mine by doing this.