Hi Vineyard Family! Ash here. A while back I was reading through the Exodus story and ran across the song of praise the people of Israel sing after the Lord brought them across the Red Sea. That song includes a line I found to be very familiar!
"The Lord is a warrior, and the Lord is his name."
I read that and thought, OH! That's where that part of the House Prayer comes from. Well then of course I had to go find where the other parts came from (researching and making lists is one of my great joys in life). It won't suprise you that each part of the house prayer is very intentional. Here's what I found, and I hope you enjoy this breakdown as much as I enjoyed putting it together!

Blessed are You, the LORD our God, the King of the universe.
Many traditional Jewish prayers begin this way, including the blessing of the passover meal and the blessing of the wine for passover. Jesus would have used these prayers himself (see Matthew 14:22 as an example, where it says he blessed the meal)
A pdf of several of these prayers can be found here.

I love You Lord with all my heart, with all my soul, with all my mind, and with all my strength.
Deuteronomy 6:4-5 - The prayer known as “the Shema” was given to Israel at Sinai and was commonly recited daily by the Hebrew people.

Our Father, who is in heaven. Holy is Your name. Your Kingdom come. Your will be done. On earth as it is in heaven. Give us this day our daily bread. And forgive us our trespasses as we forgive those who trespass against us. Lead us not into temptation but deliver us from the evil one. For Yours is the Kingdom. Yours is the power. Yours is the glory forever and ever.
Matthew 6:9-13 : Commonly called “The Lord's Prayer” or “the Disciples’ Prayer”, this is how we were instructed by Jesus to pray during his sermon on the mount.

Behold, the Kingdom of God is here…
In Luke 17:20-21, Jesus responds to the question of when the Kingdom is coming by saying the Kingdom is here in their midst.

and Jesus is Lord!
Matthew 28:18-20 (Christus Victor!)  And Jesus came and said to them, “All authority in heaven and on earth has been given to me. Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all that I have commanded you. And behold, I am with you always, to the end of the age.”
Romans 10:9-11: "If you confess with your mouth, 'Jesus is Lord,' and believe in your heart that God raised him from the dead, you will be saved".

The Lord is a Warrior and the Lord is His name!
Exodus 15:3-18 : The people of Israel proclaim this at the beginning of the “Song of the Sea” which is a song of praise to YHWH after he led them across the Red Sea and saved them from pharaoh's army.

I am a warrior in His army!
The reality that we are warriors against the powers of darkness is found across the New Testament, but some references include: 2 Timothy 2:3-4, Ephesians 6:11, 1 Timothy 6:12, 2 Corinthians 10:4

And I worship and serve King Jesus only!
Luke 4:8  And Jesus answered him, “It is written, “‘You shall worship the Lord your God, and him only shall you serve.’” We hereby acknowledge that Jesus IS the Lord in human flesh as well as the promised King.

Come Holy Spirit!
This is the famous prayer Lonnie Frisbee prayed in the early days of the Vineyard (Mothers Day 1980), and that itself was a reference to the Veni Sancte Spiritus prayer which is a traditional liturgy for celebrating the day of Pentecost and the outpouring of the Holy Spirit.

I surrender to your lordship.
2 Corinthians 3:16-18 “Now the Lord is the Spirit, and where the Spirit of the Lord is, there is freedom. And we all, with unveiled face, beholding the glory of the Lord, are being transformed into the same image from one degree of glory to another. For this comes from the Lord who is the Spirit.”

Teach me,...
We see the Lord as teacher in various places throughout scripture. Here are a few examples:
John 15:26, John 16:13-15, 1 Corinthians 2:10-14, 1 John 2:27, Matthew 23:10

…lead me,...
A common prayer throughout scirpture, most notably in the psalms (Psalms 5:8,  Psalms 25:4-11, Psalms 31:3-5, Psalm 143:9-10, etc) and in the Lord's prayer (“lead us not into temptation but deliver us from evil”)

… sanctify me.
Sanctifying us or making us holy is part of the work of the Holy Spirit: John 17:17, Hebrews 10:14, 1 Thessalonians 5:23, etc

Empower me to be a bold witness for You.
Acts 1:8  But you will receive power when the Holy Spirit has come upon you, and you will be my witnesses in Jerusalem and in all Judea and Samaria, and to the end of the earth.”

To boldly speak Your Word and Your Truth in love.  
Ephesians 4:15 “Rather, speaking the truth in love, we are to grow up in every way into him who is the head, into Christ”
Ephesians 6:18-19 “praying at all times in the Spirit, with all prayer and supplication. To that end, keep alert with all perseverance, making supplication for all the saints,  and also for me, that words may be given to me in opening my mouth boldly to proclaim the mystery of the gospel,”

While You stretch forth Your hand in many signs and wonders and healings.
Acts 4:30  “while you stretch out your hand to heal, and signs and wonders are performed through the name of your holy servant Jesus.”

All for Your namesake!
God is cited repeatedly as doing work for His namesake and calling us to do the same: Psalm 23:3, Psalm 25:1, Psalm 31:3, Psalm 79:9, 1 John 2:12, Matthew 10:22-24 among others

All for Your glory!
Habakkuk 2:14 “For the earth will be filled with the knowledge of the glory of the Lord as the waters cover the sea.” ;
1 Corinthians 10:31, which says, "So, whether you eat or drink, or whatever you do, do all to the glory of God”

Amen!
Traditional closing to prayers, literally meaning “truly” or “it is so”
See the oxford languages breakdown of this word here