Yes, and it may be that “Jesus is Lord” sounds better in the UK for the opposite reason—that we do have a monarchy. I don’t know.
Of course, YHWH is also “king” in the Old Testament, so don’t you have the same problem in principle as with saying that Jesus is Lord? In a way, it’s important not to lose sight of the continuity with the Old Testament attribution of these titles to YHWH. I think that in order to understand the lordship or kingship of Jesus we have to keep in mind that the authority to judge and rule were transferred or delegated from YHWH to Jesus to reign at his right hand until the last enemy is destroyed.