Acts 16:30-31
30 And brought them out, and said, Sirs, what must I do to be saved?
31 And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house.
Notice how simple the response is to the jailer's question about how to get to Heaven. Notice the absence of any command to "repent of your sins" (to some nebulous extent), or "submit to the Lordship of Christ" (to some unspecified degree).
Lordship Salvation is a theology that adds to the Gospel. They assert that to "believe" entails that you submit to the Lordship of Christ, and you make Him the Lord of your life. In essence, they teach that the Gospel is "submit to Jesus". That's how one is born again.
Of course, this obliterates the Gospel message. It's gone from a free gift (Romans 5:15-18, Romans 6:23, Ephesians 2:8-9, John 4:10) into a very costly lifestyle decision. Now, the entire Gospel is about you - have you submitted, how well are you behaving, have you lived a changed life.
The issue with this is that any unsaved person can behave like Jesus. Any unsaved person can quit drinking alcohol. Many people never start drinking alcohol, are they already saved? The idea that the Gospel is reforming your life (with Jesus thrown in as an afterthought) is not a Gospel at all. Gospel means good news, and it's not good news to learn that you have to reform every aspect of your life or else you will burn in Hell forever. That's horrible news, and it's also a form of what almost every unsaved person believes already anyway.
They teach works Salvation by redefining faith to mean obedience to Jesus. Faith to them is not trusting Christ, it's obeying His commandments, it's performing - your works are the proof of your faith, so we must mention them in relation to the Gospel. Wrong. In doing this, they conflate Salvation, which is free, with sanctification and discipleship - processes which take a lot of effort (Luke 9:23, 14:33). In this sense, they put the cart before the horse.
How you live after Salvation is not part of the Gospel message. Your submission to Jesus Christ is not part of the Gospel message. The Gospel message is about explaining what Jesus did for you to pay for your sins on the cross. When you understand how He was able to save you, and you trust Him to save you, you are given Eternal Life. That's the good news, that's the Gospel.
Faith and works are not one in the same. Faith is the antithesis of works in regard to Salvation (Ephesians 2:8-9, Romans 11:6), and faith without works justifies the ungodly (Romans 4:5). Doing works in accordance with that faith is a completely separate issue called discipleship, and discipleship is not required for Salvation. That's why it's possible to have "faith without works" (James 2:20), and it's why good works must be "added" to faith (2 Peter 1:5-7).
Of course, faith is a prerequisite to works that God will accept, in the sense that before we can work in the will of God we need to have faith and do that work in faith (Hebrews 11:6). But believing that Jesus is the Christ (1 John 5:1), who paid for all of my sins, and is my only way to Heaven, will not automatically cause my hands to open a Bible, or my head to bow to pray, or my feet to start walking to preach the Gospel somewhere. We retain free will after Salvation, meaning those things take a conscious effort. They take work.
Lordship Salvationists compulsively bring works into the equation when trying to preach the Gospel, because they are horrified at the thought that, otherwise, God might be hoodwinked into letting a very wicked person into Heaven. So, they do God a favor, and add to His proposition requirements that, were they consistent, would exclude even themselves from Heaven. God can take care of misbehaving Christians (Hebrews 12:6). You aren't doing Him any "favors" by adding a contract to submit and behave to the Gospel.
The general thesis of a Lordship Salvationist is - "If a person doesn't keep the Law of God to some undefined degree (like I do), and avoid some unknown level of sin (like I do), and types of sins (like I do), they don't have true faith (like I do)".
Faith in what? What gets any man or woman saved is putting their faith entirely in Jesus Christ to justify them and get them to Heaven. Does believing that mean you will always obey Christ (or obey Him to some unknown, unquantified degree that you made up)?
No, it doesn't. This is essentially a denial that someone can be a hypocrite. You believe lots of things that you don't act in accordance with, and are therefore a hypocrite. Lordship Salvationists' arguments about "true" faith are as absurd as the following:
What they mean is, "If you have real faith, you won't be a hypocrite more often than I am, according to some definition of behavior and standard that I made up". They certainly aren't going by Jesus Christ's standard of perfection (Matthew 5:48), as is covered in the article Lordship Salvationists Have No Idea How High the Standard Is.
Lordship Salvationists like to add qualifiers to sin that are not found in the Bible in order to make sure they aren't condemning themselves. They say that a believer can sin, but they can't live in "willful, habitual sin". The "willful" part of this is, to my knowledge, based on Hebrews 10:26. "Willful" here refers to a sin that you know about, which harkens back to the Old Testament Law, where there would be one punishment for sinning ignorantly vs sinning willfully. This means that, if you are studying the Bible as commanded (2 Timothy 2:15), within short order, virtually every sin will be "willful".
It does not mean that you are ever "helpless" to resist sin, which is what that verse is implied to cover by Lordship Salvationists. The Bible is very clear that you are never helpless to resist sin (1 Corinthians 10:13).
But, even if we take those qualifiers to be legitimate, the fact remains that you, and anyone else who has ever read this, lives in willful, habitual sin. For instance, any act of laziness or procrastination is a sin (James 4:17). Are you really prepared to say that you live above that? Would you survive me, or anyone else - let alone God - checking, on just that single sin?
Sin means you are breaking God's commandments (1 John 3:4) - dozens of which require action and effort. There were Christians who sinned so grievously that God had to kill them (1 Corinthians 11:30). But, to a lesser extent, all of us sin, every day. You have no idea how high the standard is if you think that you live above it, or anywhere remotely near it. The standard is Jesus Christ. Anything short of that is sin (1 John 5:17).
Lordshippers construct a fallible, imperfect standard where God allows imperfection, so that they can meet it. No. If this has to do with Salvation, God requires absolute perfection (Matthew 5:48, Romans 3:10: 1 Corinthians 6:9). That's why we are saved by faith, because faith is the means by which we receive the perfect righteousness of God (Philippians 3:9, Romans 4:6).
Lordship Salvationists deny that they teach works Salvation by attributing all of the believer's works to the Holy Spirit. That's why Lordship Salvation is inextricably linked with Calvinism. It's a denial of a believer's free will to grieve the Holy Spirit (Ephesians 4:30) and quench the Holy Spirit (1 Thessalonians 5:19).
The Holy Spirit never mind-controls you. If He did, He'd do so all the time, and you'd be perfect. It would not be an on-again off-again situation where He still allows you to sin, for some reason, then takes over and forces you to do right. This is just a pseudo-humble way to deny that you are boasting about how good you are.
The Holy Spirit will only have His way in your life if you cooperate. That takes effort on your end, since you - not the Holy Spirit - are the limiting factor. If the Holy Spirit has 100% control over every "genuine" believer, can you explain why He's doing such a lousy job? Very few Christians ever preach the Gospel to anyone. If the Holy Spirit has total control over "real" believers, why doesn't every believer live a fantastically victorious life above sin? Because it's not true, that's why.
This teaching of Lordship Salvation is Roman Catholicism dressed in Evangelical vocabulary. They deny the doctrine that every believer has two natures. They conflate discipleship with Salvation. They make works part of the Gospel, and then claim that they teach faith alone.
Lordship Salvation is the religion of Cain with Jesus thrown in as an afterthought, just like Calvinism, Catholicism, and all the rest of the groups whose Gospel is "you believe in Jesus by behaving like Jesus, so behave, and cross your fingers and hope you make it".