I think they did precisely what the Messiah taught them to do. Giving up Sola Scriptura, going by tradition or speculation, one can reason that they also recited the Shema prayer for example, and not just the first verse of which the Messiah quoted in the Gospels as the Greatest/First commandment.
Jesus teaches them this prayer, which you suggest is possibly one of two they prayed, and Jesus prays to the Father in the Garden something different??
I don't think so. Jesus isn't one to say do something and He do something else.
39 And He went a little beyond them, and fell on His face and prayed, saying, My Father, if it is possible, let this cup pass from Me; yet not as I will, but as You will. Matt 26:39
42 He went away again a second time and prayed, saying, My Father, if this cannot pass away unless I drink it, Your will be done. Matt 26:42
When Jesus prayed before the crowd prior to raising Lazarus did he offer the Lord's Prayer? No. He made a specific entreaty and prayer of thanksgiving.
Then Jesus raised His eyes, and said, Father, I thank You that You have heard Me. 42I knew that You always hear Me; but because of the people standing around I said it, so that they may believe that You sent Me. 43When He had said these things, He cried out with a loud voice, Lazarus, come forth. 44The man who had died came forth, bound hand and foot with wrappings, and his face was wrapped around with a cloth. Jesus said to them, Unbind him, and let him go. John 11:41-44
Paul had a different prayer as well.
11To this end also we pray for you always, that our God will count you worthy of your calling, and fulfill every desire for goodness and the work of faith with power, 12so that the name of our Lord Jesus will be glorified in you, and you in Him, according to the grace of our God and the Lord Jesus Christ. 2 Thess 1:11-12
Serious question: Do you ever just talk to God in your own words?