Matthew 6:9-13, the text is from the New American Standard Bible. I removed punctuation and verse numbers. Any parenthesis, I added. 

Our Father

• Isaiah 63:16 and 64:8. 63:16 – Doubtless thou art our father, though Abraham be ignorant of us, and Israel acknowledge us not: thou, O Lord, art our father, our redeemer; thy name is from everlasting. KJV
• Malachi 2:10

I thought there would be many references to God/Lord as Father. These three are the only ones I found; as I thought about that I realized that Hebrews took/take God and what they call Him very serious because of respect for Him. Hebrew Concordance: ’ā·ḇî·nū — 19 Occurrences

Who is in heaven

• Psalm 2:4, 11:4, 14:2, 20:6, (33:13 and 53:2 refer to Him looking down), 115:3, 123:1 136:26. 115:3 But our God is in the heavens: he hath done whatsoever he hath pleased. KJV
• Ecclesiastes 5:2
• Isaiah 63:15, 66:1 “My throne”; 14:12 references Satan NOT being in Heaven
• Lamentations 3:50
• Daniel 2:18,19,28,37,44; 4:37; 5:23
• Jonah 1:9

These first two lines clearly state who we are praying to and where He is. Israel was surrounded by pagans that had their gods living on a mountain or in a temple or a hole in the ground. I am glad to say these lines worked as even current pagans know where our Father lives. It would be good if you did your own wordsearch on heaven in the Old Testament. As you do make note of the Books of the Bible and the action going on around the reference. I found it interesting. I used the NIV in BibleGateway.com.

Hallowed (Holy) be Your name

• Leviticus 20:3, 22:2 and 32
• 1 Chronicles 16:10, 35; 29:16 O Lord our God, all this store that we have prepared to build thee an house for thine holy name cometh of thine hand, and is all thine own. KJV
• Psalm 30:4, 33:21, 97:12, 103:1, 105:3, 106:47, 111:9, 145:21
• Isaiah 29:23
• Ezekiel 20:39; 36:20,21,22; 43:7,8: 39:25, 7 – So will I make my holy name known in the midst of my people Israel; and I will not let them pollute my holy name any more: and the heathen shall know that I am the Lord, the Holy One in Israel.
• Amos 2:7

Please see my post Hallow or Hollow.

Your kingdom come

There was no easy wordsearch results for this petition. John the Baptist and then Jesus did proclaim this idea in Matthew. After musing on this, I became okay with that fact. For me, the foreshadowing came in Isaiah. Isaiah 2:2 has “come let us go to the mountain of the Lord” and then 2:12 is one of many references to “a day or the day”. The “Day” is referred to many times in Isaiah and the other prophets and is connected with a time to come, many of them are hard times. Another line of thought deals with “new” things the Father does, so His kingdom was always advancing. For an example: Abraham to Jacob’s sons, to Moses, to Saul, to David, to Jesus and His Church. (As I read Isaiah 11: 10-13, I had to add this reference; they are the banner of the Root of Jesse and the banner for the nations with Israelites in exile.)

Your will be done

• Genesis 28:15 a promise to Jacob
• Exodus 34:10
• Numbers 23:23
• 1 Samuel 2:32 positive for Israel not Eli
• 2 Samuel 7:21
• Psalm 22:31, 28:5, 64:9, 78:4, 118:17
• Isaiah 25:1, 13:2, 12:4 – And in that day shall ye say, Praise the Lord, call upon his name, declare his doings among the people, make mention that his name is exalted.  63:7 – I will mention the lovingkindnesses of the Lord, and the praises of the Lord, according to all that the Lord hath bestowed on us, and the great goodness toward the house of Israel, which he hath bestowed on them according to his mercies, and according to the multitude of his lovingkindnesses. (both are KJV)
• Ezekial 37:14
• Joel 2:20

These are examples of God “doing” because of unfaithfulness.

• Jeremiah 5:19, 21:12, 22:8, 23:2, 26:3
• Ezekial 5:9, 9:10, 11:21
• Deuteronomy 29:24

This search centered on the word “done”, so some translations may use different words, but the fact that God did things is present in the verses. There are multiple chapters in Isaiah that talk about “will” and how that relates to God’s people. See Isaiah 53 – 56 and 59 – 62.

On earth as it is in heaven

• Psalm 91:11, 103:20
• Isaiah Chapter 6
• Ezekiel Chapters 1-3
• Daniel 3:28, but the whole book is filled with heaven directing actions on earth.
• Zechariah Chapters 1-6 and 12:8

This part of the prayer, I believe, is best seen when angels and humans intersect, and visions or visitations to the Lord’s throne room. My list may be very small, but you can get the idea.

Give us this day our daily bread

This is a very special phrase in our prayer. It is built around the word epiousios, and it is the first time it was used in Greek writing. My Old Testament thoughts were the Manna and the Quail, giving the land a Sabbath rest and Jubilee, and the promise to Hezekiah after the Assyrians invaded Judah (that really sounds like Jubilee).

Bread in the Bible – Epiousios

Epiousios a Second Thought

Artos in the Book of Matthew

And forgive us our debts

• Exodus 34:9
• Psalm 79:9
• Hosea 14:2
• The Day of Atonement, reference Leviticus 16 and 23, and Numbers 29:7.

As we also have forgiven our debtors

For me this is a Jesus concept. There are many examples of people asking for forgiveness from Father God; use forgive in a word search. King Saul did ask Samuel to “forgive” him and join him in sacrificing but that was more for his pride than anything else. The Brothers asked Joseph, but that again was a shady deal. I may have missed examples, so let me know and I will add it to the study. I am looking for one person asking another person for forgiveness.

And do not lead us into temptation (trial)

For me this is a Jesus concept. The idea and practice of Father God leading His people has many examples, Psalm 23 and Him being our Shepherd. It is the “not lead us into temptation/trial” that is alluding me. Verse 3 in Psalm 23 is the most direct example; again, please share if you have one.

But deliver us from evil (the evil one)

• Exodus 14:13
• 1 Samuel 7:3
• 2 Kings 17:39
• Psalms 6:4, 7:1, 18:2, 56:13, 59:2, 71:4, 97:10

As I have read through Psalms, Isaiah, and the New Testament it is hard not to see how Jesus and the disciples referenced the “Bible” they knew. (Look at the footnotes, if your Bible has them.) That is the reason for this study on how the Lord’s Prayer was built from the Old Testament.