Upgrading to High Sierra or newer on 2013 MacBook Air with external SSD and missing OEM internal SSD
There are reports of other computers with a similar problem, and a damaged or missing internal drive seems to be a factor. 

From MacRumors:

"The EFI Firmware can only update using the EFI System Partition on the internal storage media. So even if you don't want to boot from it, you're still going to need a working drive in there to support firmware upgrades."

From Ask Different (this site):

"I have spoken with OWC customer service, and they say I will need to reinstall the OEM SSD. Then upgrade to High Sierra, which will update the Mac's firmware. Then re-install the OWC drive, and upgrade that to High Sierra."

So any system update that includes an EFI Firmware update will throw this error if you do not have an internal drive.

It looks like you will need to get a replacement SSD module for this Mac, which ultimately, is a better solution than running from an external.