Assuming the installation is good and you are receiving a solid interference free signal in the first place then what you are seeing are digital artifacts in the image thanks to the less than optimal bitrates used on many digital channels which are being enhanced by the LCD as the image resolution is increased.
Get a jpg and double it's size and you will get a good idea of what is going on.
PQ issues in the enlarged image are created since there simply is not enough picture information present in the original to enlarge it without consequence.
I suspect when you feed the LCD via RGB scart from a DVD source the picture is far better?
That is down to the DVD source being of better quality to begin with.
I have a 32" LCD which for 90% of the channels on SKY D does an excellent job but like most things the LCD's are not all created equal and once make/model may process a source better than another.
You can try a better quality scart and just make sure you are feeding RGB from the digibox to a RGB in socket on the LCD. That aside what are the pictures like on a "normal" CRT, if you have such a beast