Lost my AirPods case, can I get just the case replaced?

Yes. Apple sells a replacement charging case on its own, through Apple support or an Apple Store. You'll need the serial number of the AirPods themselves, which shows up on the iPhone under Settings > Bluetooth > the i next to your AirPods as long as they've been paired. Make sure the case you get is for your exact model, cases aren't interchangeable between generations. When it arrives, put both buds in the new case, charge it a bit, then hold the button on the back to pair it again.