Having done a repair something like this before (on a bigger scale) it may be possible to do something similar on this lever, if that is what it is.
The broken/snapped piece will have to be gently bent back into alignment. (Can you remove it? That would make it far easier). Firstly, to bend the broken side back into shape, place the strip in a vice and grip the strip on each edge and G-e-n-t-l-y tighten the vice a bit at a time. This has more control of the reshaping than doing it with your fingers or pliers. Then as you suggest, silver solder the broken ends together so that it retains the correct shape. If there is enough clearance on the side of the piece we are looking at, clamp a thin strip of brass or copper to the repaired strip. A slim piece cut from 15mm copper water piping will be good enough.
Cover the site with a good acidic flux and solder the reinforcing strip to the repaired section. Use plumbers solder because it is stronger than electrical solder, but still melts at a lower temperature than silver solder, so the first part of the repair wont be compromised. If you use an acid flux in wax form as used by plumbers mare sure it is cleaned off afterwards because it remains corrosive. A good scrub with an old toothbrush and water containing Bicarbonate of Soda will work.
The broken/snapped piece will have to be gently bent back into alignment. (Can you remove it? That would make it far easier). Firstly, to bend the broken side back into shape, place the strip in a vice and grip the strip on each edge and G-e-n-t-l-y tighten the vice a bit at a time. This has more control of the reshaping than doing it with your fingers or pliers. Then as you suggest, silver solder the broken ends together so that it retains the correct shape. If there is enough clearance on the side of the piece we are looking at, clamp a thin strip of brass or copper to the repaired strip. A slim piece cut from 15mm copper water piping will be good enough.
Cover the site with a good acidic flux and solder the reinforcing strip to the repaired section. Use plumbers solder because it is stronger than electrical solder, but still melts at a lower temperature than silver solder, so the first part of the repair wont be compromised. If you use an acid flux in wax form as used by plumbers mare sure it is cleaned off afterwards because it remains corrosive. A good scrub with an old toothbrush and water containing Bicarbonate of Soda will work.