Spirit of the LORD is one of the names of the Holy Spirit in both Old and New Testaments. As one member of the Trinity the Holy Spirit is often referred to in relation to the other members in names like the Spirit of God and Spirit of Jesus.
It was as the Spirit of the Lord that the Holy Spirit came upon Jesus the Messiah anointing Him for ministry as prophesied by Isaiah.
Spirit of the LORD in Hebrew:
Strong’s Concordance numbers: 7307, 3068
Bible references: Judg. 3:10; 1 Sam. 16:13; Isa. 11:2 (24X)
Samuel took the horn of oil and anointed him in the presence of his brothers, and from that day on the Spirit of the Lord came powerfully upon David. Samuel then went to Ramah. (1 Samuel 16:13 NIV)
The Spirit of the Lord will rest on Him,
The spirit of wisdom and understanding,
The spirit of counsel and strength,
The spirit of knowledge and the fear of the Lord. (Isaiah 11:2)
Spirit of the Lord in Greek:
To pneuma tou kyriou
Strong’s Concordance numbers: 4151, 2962
Bible references: Luke 4:18; Acts 5:9; 8:39; 2 Cor. 3:17
The Spirit of the Lord is upon me, because he hath anointed me to preach the gospel to the poor; he hath sent me to heal the brokenhearted, to preach deliverance to the captives, and recovering of sight to the blind, to set at liberty them that are bruised, to preach the acceptable year of the Lord. (Luke 4:18 KJV, which quotes Isaiah 61:1)
Similar names of the Holy Spirit are Spirit of God, Good Spirit, Spirit of Jesus, and Spirit of Christ.