You mention HPC and Big Data processing as use cases for EFS; Lambda is also very well suited for big processing tasks you want to execute quickly with a large amount of concurrency. You often need persistence across executions, for example when breaking tasks into multi-function workflows, and EFS would seem to simplify this over manually using S3 for it.

One use case would be one that came up a while back here on HN -- The person had a large binary blob that they needed to load up every time their Lambda function ran. If they could mount EFS from Lambda, they could put the large binary blob there.

Depending on how they wrote their code, if the Lambda could seek to the right part of the file then this would work, but if it has to load the entire file into RAM anyway, then it wouldn't gain them much except perhaps a slightly easier way to get the file into RAM.

I want to run the Elm compiler in a Lambda, and maintain persistent environments so that subsequent builds can benefit from keeping the libraries and intermediate files available.

I would like to have a media pipeline where a media goes through QC check, thumbnail, preview generation and some other processing which are independent of each other. My media can range from 1-15GB, so if I can store it in EFS which can be mounted in Lambda, I can use various Lambda functions which can simply read from a common storage without downloading every time from S3.