Since you were flying SIN-KUL-MYY, KUL-MYY is a domestic sector, you need to go through Malaysian immigration etc to take the flight.
When you were rejected from entering MH and CX lounges at KLIA, because you were trying to access the lounge as an arrival lounge after your SIN-KUL flight. Then you shall clear immigration to enter Malaysia at KUL. Based on your onward flight, which is KUL-MYY, a domestic flight, you should only be in the domestic terminal.


Because KUL, (and also SIN), international arrivals and departure passengers are not separated. Most ther airports such as BKK, HKG, NRT
have departing and arriving passengers on separate levels, so those cases would have no chance to go near the lounges.