Yes, you took an oath, but whoever you gave that oath to you should be able to release you from that oath. If you're staying in the same duchy, and you're being appointed to a new lordship, then it would stand to reason that the person who holds that oath is releasing you from it, so you shouldn't incur an honor penalty.
No, you have misunderstood.
The oath a Lord swears is to
his people. Everyone in the region. It is an oath to protect them. Stepping down means that you are abrogating that oath.
No one can release you from it.
Once you accept a Lordship, stepping down is, and should be, seen by its people as an admission that you cannot or will not protect them.