"Yes, my lord?" always had a...robitic quality to me when they said it. "Happily your highness" has more nuance and feeling, not to mention, fits better with the modern viewers who will be watching (I can't remember for the life of me, the last time a member of royalty was refered to as 'Lord" unless it was one of their titles, the reference is always his/her highness.
(no subject)