Lost one side of AirPods, buy another side to complete the pair

TLDR: Yes it's quite possible a used AirPod (only risk is incompatibility) can be paired to your current AirPod by following these directions (quoted below).

Apple's If your AirPods are lost article is a good starting point (originally linked by IconDaemon).

Before seeking a replacement, make sure you've attempted to find the missing AirPod using Find My iPhone.

If you need to replace it, Apple recommends you "get the serial number and then contact Apple Support for a replacement" - presumably to make sure their versions are compatible.

Regarding setup, you can check out Set up your replacement AirPods or charging case:

1. Put both AirPods in your charging case.
2. Open the lid and check the status light. It should flash amber.
3. Press and hold the setup button on the back of the case for 5 seconds. The status light should flash white. If it still flashes amber, connect the case to power, close the lid, and wait 10 minutes.
4. On your iPhone, go to the Home screen.
5. Open the case—with your AirPods inside—and hold it next to your iPhone. A setup animation appears on your iPhone.
6. Tap Connect, then tap Done.

If you're interested in buying a replacement directly from Apple, you can find more information under AirPods Repair (note that this is US specific, you can find the locale specific page here), where they list a replacement of a lost AirPod as costing $69 + tax + $6.95 shipping fee.

I personally would not want to use somebody's used AirPod, but if necessary I would clean out the earwax and wipe it down with a tissue soaked in hand sanitizer.

I have had a long journey with an apple replacement airpod not wanting to pair with the other. I got the following response, after calling them, which to my surprise actually worked:

1. Make sure the AirPods are unpaired by going to Settings Bluetooth AirPods Tap the (i) Forget this Device on the companion iOS device (this step is important).
2. Connect a lightning cable to the customer’s Charging Case and connect to a power source.
3. Place both AirPods in the case and put them within 4 inches of their iOS device (be sure they are not on/using the phone during this part).
4. Close the lid and wait 35 minutes. It is very important to wait the full 35 minutes with the lid closed. If this process is interrupted at all, it has to start over completely.
5. After the full uninterrupted 35 minutes, open the Charging Case lid.
6. Press and hold the “setup” button on the back of the AirPods charging case until the status light flashes white. This may take up to a full minute.
7. The AirPods should now be ready to be setup through the standard setup process

I am wondering if this process also works if two diffrent AirPods with diffrent serial numbers which in this case would fix the many "can i buy a used one to replace my lose one ?".