An alternative approach
Bill Houghton, sunny Sebastopol, CA
>I've removed a lateral lever by filing the rivet at the back side until the remaining "mushroom" was thin enough to break off when I drove the rivet out. You need to support the lever and frog well when you do this - take a chunk of metal (ideally) or hardwood and drill a hole the size of the rivet head in it. Best is to have a buddy who holds the frog upside down with the rivet head over this hole while you drive the rivet out with a pin punch.
Most hardware stores have a variety of rivets from which you can choose one to rivet the lever on its new home. Iron rivets are a softer iron/steel than nails and suchlike, so better for their purpose. Brass and aluminum rivets are also selected for being soft enough to hammer easily.
Note before you start: look at the frog on which you're planning to put this lateral adjuster lever and make sure the place where you'll rivet it is still present and willing to serve. I've seen a few frogs on which the lateral was missing because that whole section of frog had broken off.