"Lean on" is used here in the sense of relying upon or trusting someone or something for help or protection. The object of our secure trust is the Lord, a most reliable object of confidence!
When we lean against a wall or on a cane, we trust it to support us. If it should fail to do its job, we will fall to the ground and perhaps be hurt. In a figurative sense, in times of distress we lean on members of our families or friends; we rely upon them for encouragement, support, help, or protection. In this verse, "lean on" functions figuratively. Relying on our own understanding is compared to leaning on a cane that cannot bear our weight; it is unreliable for support. It is dangerous for a person to rely upon mere human wisdom or understanding because it is likely to fail him.
Acknowledging the Lord in all our ways means keeping Him in mind in every event of our lives. Godly living is not to be confined to the Sabbath, for God is involved in each moment of each day. His instruction covers our lives from waking up in the morning to going to sleep at night. He wants us to remember Him all the time and to trust and obey Him to guide our conduct in everything we do.
That "He shall direct your paths" suggests that God will "smooth" or "make straight" the road of our lives. This is a promise that God will go before us and remove many of the obstacles from our path. He wants us to be successful, so if we trust Him and follow His instructions, He will lead us forward, sweeping many of our potential problems to the side. How encouraging!
My Parents Won't Let Me!
These verses contain the first principle upon which all our work and hope depend. In every aspect of life, we must take God into account. We should seek His counsel regarding our home, community, work, and play. This is not an elective but an absolute necessity, so the relationship established through Jesus Christ influences our conduct to the point that it is according to His will. This requires humility, but if we remember that He made us, and we are dependent upon Him for everything, the proper attitude comes easier. If we do not do this, we are foolishly failing to acknowledge the One whose thoughts and ways are higher than heaven is above the earth. All of our ways are in the hand of this Almighty Sovereign; success and safety are of the Lord. We of all people do not want to end up fighting the Almighty when He causes changes in civil government or in the church. They may appear on the surface to be working against us, but who is ruling?
Recall some examples from the Old Testament: Nimrod attempts to build a tower and unite all of mankind under one government, but God sweeps it away by the simple expedient of making communication too difficult. Esau burns with anger against Jacob, but when next they meet, he weeps for joy at seeing his brother. Joseph goes into Egypt a slave and spends time in prison based on a false charge, but as a result of God's blessing, he ends his life reconciled and reunited with his family and second in command of all Egypt. Israel is a slave people in Egypt, the most powerful nation on earth at the time, but God devastates it through supernatural occurrences—Israel is freed without "firing a shot." Balaam is hired to curse Israel, but God compels him to bless. Haman builds a gallows for Mordecai, but is hanged from it himself. Jonah resists God's command to preach to the hated enemy, the Assyrians, but God prepares a great fish just for him!
Understanding this, David writes:
Why do the nations rage, and the people plot a vain thing? The kings of the earth set themselves, and the rulers take counsel together, against the LORD and against His Anointed saying, "Let us break Their bonds in pieces and cast away Their cords from us." He who sits in the heavens shall laugh; the LORD shall hold them in derision. Then He shall speak to them in His wrath, and distress them in His deep displeasure. . . . "You shall break them with a rod of iron; You shall dash them in pieces like a potter's vessel." (Psalm 2:1-5, 9)
God is infinitely stronger than even the greatest of confederacies, and He will blow away the most extensive and vigorous efforts to overthrow His plans like so much dust. He laughs at man's puny attempts to rule without considering Him, their Creator, in whom they live and move and have their being. Will He who repulsed the attacks of Satan's mighty angelic host be put in fear of more limited men?
John W. Ritenbaugh
The Sovereignty of God: Part Five