Albert Barnes on Matthew 22:43

How then, etc. How is this doctrine, that he is descended from David, consistent with what David said when he calls him Lord? How can your opinion be reconciled with that ? That is recorded in Ps 110:1. A lord or master is a superior. The word here does not necessarily imply Divinity, but only superiority. David calls him his superior, his Lord, his Master, his Lawgiver; and expresses his willingness to obey him. If the Messiah was to be merely a descendant of David, as other men descended from parents--if he was to have a human nature only, as you Jews suppose--if he did not exist when David wrote-- with what propriety could he, then, call him his Lord?

In spirit. By the inspiration of the Holy Spirit. As a prophet, Acts 2:30, 1:16, 2Sam 23:2.

(o) "call him Lord" Ps 110:1, Acts 2:34, Heb 1:13, 10:12,13