KUL is like that, and the first time comes as a shock. But the next time you pass there, you will be wiser.
I personally just stick to the MH lounge.
OR, get two boarding passes (home print + airport BP). Show the home print to the MH lounge (home/mobile BPs accepted), and the airport BP to the Contract lounge/Cathay Lounge (these two insist on the airport BP, to enforce the 1 lounge limit).