Turns-out JST works under Kickstart 1.3 and seems to play the Lemmings 2 WHDLoad slave without any issues I could spot with a very brief test:
http://jotd.pagesperso-orange.fr/amiga.html
Edit: Oh, wait, it gurus if you try to exit
I used JST 6 with KS 1.3 (patched to 1.3.2) under workbench 1.3.2 with an OCS PAL Amiga 500 (with plenty RAM) and the 1.6 version of the WHDLoad Lemmings 2 slave.