Consider the Hebrew words in this verse. “JEHOVAH said unto my Lord (Adon), Sit thou at my right hand, until I make thine enemies thy footstool.” 

“Adon” is Strong’s word H113 and it is a general term meaning “mighty one.” It is used throughout the Old Testament to refer to rulers, judges, people with power, the angels, the Logos, and even to God Jehovah. Adon is used 329 times in the Old Testament.

Here are two examples where the word Adon (Lord) is applied to both angels and man. 

When the three angels came to visit Abraham, they were called Adon. Genesis 18:3, 12 NKJV), “and (Abraham) said, "My Lord (Adon), if I have now found favor in Your sight, do not pass on by Your servant. Later in Genesis 18:12, Sarah called Abraham Adon. Verse 12 “Therefore Sarah laughed within herself, saying, ‘After I have grown old, shall I have pleasure, my lord (Adon) being old also?’”

So, yes, in Psalm 110:1, Jehovah is talking to David’s Adon, Jesus.

David is prophesying that Jehovah will tell the risen Lord Jesus that through the power Jehovah gave Jesus in His resurrection, all of His enemies will be subdued. Matthew 28:18 (KJV), “And Jesus came and spake unto them, saying, All power is given unto me in heaven and in earth.”