For dual sliding doors without a mortised lock, you'll often see people chaining the handles together, and fastening the chains tight with a padlock. That solution is somewhat effective, but inelegant and janky; you've got to take all of the slack out of the chain each time you lock it to ensure a good seal, and when unlocked, the chain hangs sloppily off of the handle.

Here's a better-looking and -functioning solution I came across. You still need the padlock, but you can do away with the chain, plus ensure the doors are sealed shut:

I was unable to find the original source, so if any of you know whether this is off-the-shelf or DIY, please drop a line as I'd love to credit the inventor.