Yes, unless you find premises to drop, thus changing the problem. Sorting is Omega(n log n) under the premise that all you have is a computable ordering relation. Radix sort removes that premise and reaches a different lower bound.

In the particular case of the Hanoi problem, I don't see droppable premises (except "you can only move one disk at a time" -- drop that and there may be an O(1) solution).