Satan has 0 rule in heaven, it's God's uncontested domain. If Gods will be done on earth, there would be no satanic influence. It's a plea to not let Satan rule in us or on earth. We can only work on ourselves to allow Christ to dwell richly in us. The day hasn't come yet where Satan has no rule on earth. Just look around you lol !! Additionally it's pretty much a daily plea, let each day be made new in Christ Jesus for we know not what a day brings.
The Lords prayer while a good prayer in and of itself was to be an example, an outline of how to pray, that's why Jesus said to pray in like manner. IE, hit all those topics in your prayer life. He didn't say to recite this prayer. I've heard some great sermons on how to pray like the Lords prayer but not reciting the Lords prayer, where the pastor expanded on each topic within the prayer itself.
That said, when reciting the Lords Prayer we feel peace don't we ? We are aligning with Him if we pray it with meaning in our daily walk and not just a canned response . And that's really the point of the whole thing. We always need to align or agree with God, this needs to be in our hearts, that desire. We don't do that perfectly here on earth, they have it nailed down in heaven.