It's not possible the Python27.dll would be missing after the Live Udpate, since it's one of the files that belongs to the Addon Manager so, it will be downloaded by the Live Update if it was missing for some reason.
Of course, I tried it now: I removed the file Python27.dll manually, and then I ran the FSDT Live Update and, sure enough, it downloaded it again, because it found it missing.
The only possible reason of the program missing, it's the interference of a bugged antivirus program, which might have removed it mistakenly assuming it might be dangerous (it obviously isn't, it's the Python runtime...), so first it removed it, and then it blocked the Live Update that was correctly trying to restore it.
- Configure the antivirus to exclude the whole Addon Manager folder from scanning
- Run the Live Update again.