How does one enforce a secure lockscreen on Android mail clients?
Seems the answer is, "it can't be enforced", despite the non-answer that user157947 gave. (Seriously, did you actually read the question?  You certainly didn't read or respond to my follow-up queries.)

The closest one might come to this is to use custom CA certificates for signing the TLS key used by IMAP, as installing the requisite CA certificate (for server verification) in the phone more or less enforces the key lock.  Another option is to issue client certificates for each device to be connected via IMAP: this too enforces a secure screen lock.

Microsoft Exchange is able to enforce it by means of proprietary extensions in the protocols used it seems, it is not done over IMAP/SMTP.