It's certainly possible. It's complicated, though, by the double curvature of the stern, and the (usual) presence of the boarding ladder on the stern. (An outboard could potentially be located offset to one side or the other of the boarding ladder.) One would probably also want the throttle and gears to be controlled by cables, as it would likely be difficult to reach the outboard due to the stern's height above the water, and the presence of the aft deck on the LM27.
I don't know of anyone that's done it. I have a vague memory that I read somewhere of someone temporarily mounting a small outboard on something attached to the boarding ladder (but perhaps that wasn't an LM27?). I have wondered about similar (or a mounting on one side of the boat amidships), as a potential temporary 'get you home' arrangement.
In my view, getting the inboard engine working and reliable is a more realistic and satisfactory proposition for an LM27, but others will have their own priorities/challenges.
Thanks for the response, totally agree with your point reference having a reliable inboard, I was thinking of the outboard as a belt and braces stand-by. Just getting familiar with the LM27 so considering the options.
I have the same wish and idea for my LM28 but did not find any advise or good solution. If you find something, please let me know. I was tempted to fix a plate to the outboard ladder but believe this is too risky
I have done it. It sucked. Inboard engine didn't work and I couldn't fix it. The 2,5 hp Yamaha short shaft would get me up to about 3 knots. I drove about 100 km over canals / rivers. The slightest wave or even both passengers moving to the bow would make the propeller pull air. Of course a long shaft would have been way better but I could imagine it would also lift the prop too far out of the water in waves. It was mounted to the boarding ladder by a diy adapter. Unfortunately I don't have a close up image of that.
I have a similar bracket which fits over the ladder rungs. It is not ideal but it will get you home if there is no wind. I also have an emergency steering system which fits in the same way... one never knows!