May be it helps somebody, I think that I found the reason of "Disk quota exceeded" error. Here is the cut from AWS EFS manual:
Command Fails with “Disk quota exceeded” Error
Amazon EFS doesn't currently support user disk quotas. This error can occur if any of the following limits have been exceeded:
Up to 128 active user accounts can have files open at once for an instance.
Up to 32,768 files can be open at once for an instance.
Each unique mount on the instance can acquire up to a total of 8,192 locks across 256 unique file-process pairs. For example, a single process can acquire one or more locks on 256 separate files, or eight processes can each acquire one or more locks on 32 files.
Apparently we hit the limit for 256 locks per process. I checked with lslocks and indeed ES locks a lot of files.