Searching the web for
official manuals, it would appear that P for pause was supposed to work on both Amiga and Atari, for both 1- and 2-player levels. At least there was nothing in the manuals that suggested there should be any difference between keyboard control on Amiga vs Atari, nor any difference between 1-player and 2-player modes (at least for pause). I tend to suspect the inability to pause via keyboard in 1-player Atari is more likely an unintentional bug than anything else.
Granted, not every means of control is mentioned in the manual, for example the "hold right button and left-click to select walkers" ability is nowhere mentioned in the manual as far as I can see. So I can't rule out the (highly unlikely) possibility that there are some other keys that work for pause on Atari ST 1-player.
It would be interesting to see what happens with later Lemmings-1 based games on the Atari. For example, if there is a Atari ST version of ONML, does it still have the same problem or might it have been fixed by then?
Other things to try (which probably won't help, but you never know) if you haven't already:
- What happens if you first go into a 2 player level, then finish/abort it, and then go to a 1-player level?
- I assume you already configured the emulator to have both the mouse and joystick plugged in when starting the 1-player level?