A linen shirt is the base for the garb of the lord. He is also wearing braies, a medieval kind of underwear. This was a privilege known only to the men as the women did not have anything underneath besides their underdress. 

Lord Randall´s shirt resembles the Shirt of Arras, a type of shirt also worn by Lord Thomas Becket as he later became Bishop of Canterbury. He was said to have worn that shirt as a shirt of repentance until his last day. Never washed it, never took it off....

Mmmh... we DO however wash our clothes as needed ;)