How can I store things in lead bins?

Solution 1:

Dump the wooden bins with the gems in them, then reclaim only the gems within the bins, not the bins themselves. At that point, your dwarves should pick the gems out of the wood bins and put them in the stockpiles full of lead bins.

Solution 2:

It's time consuming, but the easiest way I've found to do this is to individually mark the gems themselves for dumping (or mass dump via the stocks screen. Your dwarves will swarm out, throw the gems into the nearest garbage zone, and move on. Then it's simply a matter of reclaiming the gems with d-b-c and forbidding everything but the lead bins you want them stored in.