Putting it in very simple terms. Imagine a switch- the output of the switch goes to your light. When the switch is open- ie off- there is no voltage on the output terminal of the switch that goes to the lamp.
So if the supply to the dining room switch was taken from the output of the lounge switch you would get the symptoms described. Shifting the dining room supply wire from the output to the input of the lounge switch would solve this.
This is the most basic solution to your problem. If you are happy playing with electrictiy- isolating the mains, identifying which cable is which etc then carry on- if you have any doubts whatsoever get someone who knows what they are at to have a look.
it certainly sounds as if dining room light is linked from lounge switch as burnhal says, have a look at how the lounge switch is wired, it might be as easy as he says, if there is only one wire in and one out, call in a sparky, good luck, Ray