Huh there you go, I thought all 4-speed 240s were M45 except maybe 1974/75 models.
If you want a super clean install, you should also get the ECU mounting bracket and drivers kick panel from an LH-2.4 240. It will bolt right into your '81 model! Not strictly necessary of course, you can just cable tie the ECU to something in a pinch, although I'm sure I will annoy some punters by saying that!
You will need a solution for the speedo signal, I converted a 1981 240 to LH-2.4 but I decided to just take the entire rear axle and suspension from a '92 model and so I wired up the OE sensor. You'll want an LH-2.4 instrument cluster although if you decide you don't care about the idle issues then you can ignore the speed signal input.