Not just for lost people only, also, every Christians, all shall bow down before the Lord. In Phil. 2:10-11 say, "That at the name of Jesus every knee should bow, of things heaven, and things in earth, and things under the earth; And that every tongue should confess that Jesus Christ is Lord, to the glory of God the Father."
It tells us, all people from heaven, earth, and hell, EVERYONE will bow before the Lord, confess that He is the Lord. That will be at the Judgment Day.
Notice Romans 14:10 tells us, we will all stand before the judgment seat of Christ. So, next verse 11 says, "For it is written, As I live, saith the Lord, EVERY knee shall bow to me, and EVERY tongue shall confess to God."
It is very clear telling us, all Christians will bow before the Lord at the Judgment Day, confess that he is the Lord, even, every lost people will bow before Christ, confess that He is Lord.
That is not force. Once, everyone will see Lord appears in glory and power at second advent. No question, they all will be fear and trembling, because they will realize that he is very holy and power. That will cause them to bow down before Christ.
Lord means master.
Every person of the world will be realize that Jesus is the mostly exalted name and the truly King or Mesisah. They will bow before him for sure with NO force.
In Christ
Rev. 22:20 -Amen!