What does Luke 6:49 mean?
Luke ends Jesus' Sermon on the Plain with a warning to those who call Him "Lord" but don't obey Him (Luke 6:46). In short, those two descriptions are mutually exclusive. Saying you follow Jesus while refusing to obey His commands is a contradiction in terms (John 14:15). Following Jesus requires faith in Him. The natural and inevitable result of having faith is obedience. Anything else is dead, foolish deception, not saving faith (Romans 6:14–20).Jesus has broached this topic before with the Pharisees. He said, "No one tears a piece from a new garment and puts it on an old garment. If he does, he will tear the new, and the piece from the new will not match the old" (Luke 5:36). In that context, He was saying that it is impossible to persist under the Mosaic covenant by adding a bit of what Jesus teaches. Here, He's saying that you can't label your lifestyle "Jesus-follower" if you never change your lifestyle.
Someone who obeys Christ has proven their faith is deep: they will remain steadfast even when confronted with hardships. Those who do not obey prove their faith is weak: sitting on the surface of unstable ground. The unrelenting deluge of troubles will erode the ground out from under their lives, and they will crumble.
In the next section, Luke introduces a handful of people outside privileged society who have or need that firm foundation. The Gentile centurion, the sinful woman, and the women who support Jesus financially prove their faith with acts of obedience and trust. John the Baptist's disciples show how difficult it can be to maintain obedient faith and not succumb to fear. Even so, Jesus praises John's ministry and his call to obedience (Luke 7:1—8:3).