The Lord of the Chaos Die could be a personified version of the dice themselves. It could either be a bag or box with limbs or all the dice could come together to create the form of a body (I like the latter). Name options: They Who Roll, The Roller of Dice, Themprex of the Unexpected, Majesty of Mayhem, The Cubed Maelstrom (or maelstrom as a different concept), Sovereign of Sides, Clitter-Clatter...
A dice face idea could be around wrong timing. The symbol could be a broken clock or something. It indicates that now is NOT the time to do this reading. Maybe the reader isn't in the right state of mind or the querent can't handle the truth at this time. Perhaps the astrology is a bit whack and you can diagnose when a better time would be. It could mean a five minute break to center oneself or it could mean to wait until the planet ruling over the question is out of retrograde.
Another one could be that the reading is "mirrored." It's showing the similarities between two different things. It could be that the future is a reflection of a past, as shown by the dice. It could be that in the dispute you are reading about, you and the other party are really coming from a similar space, as indicated by the dice. The point is that the concept of reflection and symmetry needs to be considered.
A fun one could be a witch-themed one. You are casting a spell to create a change in the world. Do the reading as normal and when you identify a stuck point/problem/whatever, take that die and shake it up in a pointy hat, mini-cauldron, crystal pouch, chalice or just the most magical object you have that suits the purpose. Do this with the intention of creating a favorable change. Then roll it by pouring it out from its receptacle. That factor has now changed. Even if you get the same face, it will likely be on a different spot on the board.