How likely is it that a hard lymph node is serious?

It depends: Hardness may be caused by the fact that the lymph node is scarred from an old infection, so it's not necessarily a sign of current disease. One has to look for other clues at the same time: size, mobility, rate of growth, pain, tenderness, etc. And of course other general signs of illness. All these factors come into play in determining the cause-and hence seriousness-of a swollen node.