In response to your question, anything that becomes something that you must first do prior to God granting you eternal life becomes a work of righteousness that the Bible explicitly contradicts - Ephesians 2:8-10; Titus 3:5-6. Hence, to believe that you must make Christ Jesus Lord before you can be saved is false doctrine. However, on the other extreme, there are those that teach that all you have to do is ask God to forgive you and you're saved. This too, is a form Arminianism - and depends on something you do.
The better approach to the matter is to understand that a sinner (prior to saving grace) is totally dead spiritually. A dead thing can do nothing to help themselves. Salvation is not a result of my asking God for something (that becomes a work) - it is a result of the mercy and grace of God that is given to me whereby I am "made alive together with Christ (by grace you have been saved), and raised us up with Him, and seated us with Him in the heavenly places in Christ Jesus." - Ephesians 2:4-6. When a person is quickened by the bestowal of saving faith, the very first result is an awareness of personal guilt before God whereby God's Spirit convicts of "sin [personal], righteousness [belonging to Jesus Christ alone], and judgment [that must result because of the justice and holiness of God]." - John 16:7-8.
The very first response of this newly quickened heart, that has a deep awareness of the offense of their sin to a holy God - is to fall on one's face before that holy God and seek forgiveness (commonly called by some "the sinner's prayer"). However, understand that a person can vainly "say the words" of repentance without God having done a work of grace -- all of which results in a religious zeal, but remains void of effect. This is what James calls "faith without works." (James 2:18-26). When a person has received the gift of saving faith from God, his life is changed. His heart is yielded to His God and as a result yields to the Lordship of Christ. I believe that this will be the fruit of every genuine work of grace in a person's heart. Notice, yielding to the Lordship of Christ is a result, not a cause of genuine salvation. There are many who believe they are saved because, in a moment of religious affection, they professed the name of Christ, without knowing the drawing of God's grace - John 6:44. Such one's are professing Christians, but have no genuine confession of Christ - cp. Matthew 7:21-23.
It is possible to fail to grow as steadily as you should. Carnality is merely a believer who is behaving "fleshly" and can occur. However, such a one will encounter the disciplinary hand of God - Hebrews 12:4-11. We are told a number of times that God will even go so far as to take a person home to heaven in discipline - 1 Corinthians 11:30-32. Verse 32 indicates that before we would ever lose His grace, He will do take our lives. This is consistent with those passages where Christ tells us that "all that come to Me I will not cast out." - John 6:37. We are secure precisely because our salvation is the work of God - not ourselves. In the same way, our sanctification is the work of God - we yield ourselves to Him and He perfects us through His grace. In regard to this, someone once said: "If your faith fizzles before the finish, it was faulty from the beginning!'
I trust this helps clarify the issue for you. Remember, salvation is the work of a gracious loving God who "chose us in Him before the foundation of the world, that we would be holy and blameless before Him. In love He predestined us to adoption as sons through Jesus Christ to Himself, according to the kind intention of His will, to the praise of the glory of His grace, which He freely bestowed on us in the Beloved." - Ephesians 1:4-6.