You will need a transformer to convert the 240v mains to 120v for your enlarger. It would be best to use a 120v Analyser Pro, so you'd plug the transformer into the 240v mains, plug the Analyser into the 120v from the transformer, and plug your enlarger into the Analyser's Enlarger socket. Alternatively (and this would be a better solution) you could find a 240v version of the LPL power supply. The Analyser is simply a mains switch so no, you cannot plug your 120v enlarger into a 240v Analyser.

Is your enlarger a colour or VC head? They use (I think) a 24v lamp so you'll already have a transformer to convert the 120v to 24v - the best solution is to replace that with a 240v-24v transformer.