I haven't flown out of the Melbourne on MAS so can't comment.
But in KL you will have access to the Golden Lounge in the satellite terminal. Almost all long haul Malaysian flights arrive and depart from the satellite terminal. The Golden lounge is located upstairs. Gold/Business class entry on the left, platinum/first class on the right. Is a fairly big lounge. It can get busy at certain times and days and be quite empty at other times. Has a pretty good selection of foods and drinks. There is a barista serving coffees. They use to have free massages, now I think you have to pay for them. There is wifi, which is fast and works well. The lounge is starting to show its age, it could do with a refresh.
Last year Frommers ranked it the 3rd best lounge in the world. It is good, but not that good.
At KLIA there is also a regional lounge (short haul international) in the main terminal which you could access. But the satellite one is better than the regional one. Also a domestic lounge at KLIA if you are flying domestically.
At LHR the lounge is in Terminal 4 and still quite new at about 3 years old. Has a selection of food and drink. It is a good airline lounge, but nothing spectacular.