How would a lord go about redesigning his sigil and/or changing his words? Can he do it on a whim, or does the new design have to be confirmed by a higher authority?

Well, personal sigils seem to be fairly easy to change – hence Littlefinger changing his sigil to the mockingbird, or Garlan and Loras taking a number of golden roses on green.

But as far as I can tell, there’s nothing stopping a lord from changing their sigil at any time – as long as other people recognize their sigil, which is the point of having them in the first place. As long as they’re actually a lord and their sigil doesn’t copy someone else’s without cause, I don’t see the college of heralds having a problem with it.