While J-B Weld is one of my favorite products, it's not nearly strong enough to put an end back on a handlebar lever.
This repair could be done, however, with low temp
aluminum brazing rod. It's available by the pound, fractional pound, and even individual stick, at hardware stores, NAPA stores and I think welding supply stores. You can also find it at various trade and hobby shows, such as gun shows, model plane and train shows, ect.
The key to using it successfully is preparation. Clean the metal to be repaired very well (remembering that the higher the aluminum alloy, the faster it re-oxidizes). Heat the broken piece on a hot plate, in an oven (or, in Arizona, let it lie out in the noon day sun). Aluminum sucks the heat out something fierce, so keep it hot while you solder.
If the broken piece is small, a propane or MAP gas torch can be used. If the piece is big (lots of bulk), you may need to use an oxy-acetylene rig. Remember, you're not "welding", i.e. melting, the parent metal, you're just "brazing" it. Vee grooving the crack line/broken mating surface is usually very helpful.
Nothing beats TIG (Heli-Arc) welding, but this comes close, and is a heck of a lot less expensive.
