The idea is, “Because chastening is thus necessary, and serves for a wholesome discipline, and issues in holiness” therefore...you are in the race of life...maybe you are growing faint and losing heart because of the variegated trials, conflicts & afflictions that you are experiencing...but now....now that you know the nature of your conflict is discipline and that this discipline is to be received and endured because it emanates from the heart of love of our heavenly Father, Who is treating us as His sons...and that the results of subjecting ourselves to His discipline include life, holiness, peaceful fruit of righteousness...therefore....knowing all of this truth...exert effort...lift up those hands and feet...start pumping...you're in a race with eternal rewards...expect agony, expect conflict, expect discipline but realize the goal of it all is an eternal weight of glory far beyond all comparison (2Cor 4:17)...and so also expect VICTORY, expect REWARD, expect that a tried & approved faith will receive great glory at the revelation of our Lord (1Pe 1:7).

Also because they are in need of endurance (see note Hebrews 10:36)...they need this exhortation. It's like a coach on the sidelines calling out the lap times...saying hold that pace...you're on a pace to finish the course...there's only a few laps to go and you can enter His Rest! (see note Hebrews 4:3)

The experience of “hitting the wall” in a Marathon is a picture of weak hands, feeble knees... The exhortation implies that the readers are acting as though spiritually paralyzed.

This means to restore to straightness or erectness, to reinvigorate. The command to “strengthen” comes from the word from which we derive our English word orthopedic. The sense is, “make upright or straight”—or in modern coaching terms, “Straighten up! Get those hands and feet up! Suck it in!”

Weak hands and feeble knees was a common description of weakening and slackness (cf. Isa 13:7; 35:3; Jer 47:3; 50:43; Eze7:17; 21:7; Zeph 3:16, Job 4:3,4)

Stedman explains this verse noting that the writer is calling for his readers to...

deal first with yourselves. Get your own hearts right toward your troubles. He has already pointed out the way to do so: by each coming boldly to the throne of grace “so that we may receive mercy and find grace to help us in our time of need” (see note Hebrews 4:16). He has said the same in Hebrews 12:2: “Let us fix our eyes on Jesus, the author and perfecter of our faith.” It is only as we know his help ourselves that we are able to aid anyone else in finding it. The plural imperative (strengthen, Gk “lift up”) implies a joint effort by many. We can help each other draw upon the resources of Christ by offering encouraging words and mutual prayers, sharing our experiences and sometimes simply being with someone who is under going trial.

Of course, the important thing is how God’s child responds to chastening. He can despise it or faint under it (Heb 12:5), both of which are wrong. He should show reverence to the Father by submitting to His will (Heb 12:9), using the experience to exercise himself spiritually (Heb 12:11; 1 Ti 4:7-8). Hebrews 12:12–13 sound like a coach’s orders to his team! Lift up your hands! Strengthen those knees! (Isa35:3) Get those lazy feet on the track! (Pr 4:26) On your mark, get set, GO!

The example of God’s Son, and the assurance of God’s love, certainly should encourage us to endure in the difficult Christian race.

Happy is he who knows how to sustain with words him that is weary (Isa 50:4). Happy is he who accepts exhortation (Heb 13:22). And thrice happy is he whose faith is simple and strong so that he finds no occasion of stumbling in the Lord when His discipline is severe

Quoting from Pr 4:26,27, cp Jer 18:15 cp highway of holiness Isa 35:8

Make (4160) (poieo) means to do expressing action either as completed or continued. The verb is in the present imperative which is a command for us to continually make the paths straight. This speaks of our responsibility in the race of life so that we are enabled to run with endurance.

Lame (5560)  (cholos) speaks of a spiritual limping, and in particular, to those among the recipients who were most seriously affected by the persecutions, and who were on the verge of going back to the temple sacrifices.

Wuest has an interesting comment:

"The exhortation is to the born-again Jews who had left the temple, to live such consistent saintly lives, and to cling so tenaciously to their new-found faith, that the unsaved Jews who had also left the temple and had outwardly embraced the NT truth, would be encouraged to go on to faith in Messiah as High Priest, instead of returning to the abrogated sacrifices of the Levitical system. These truly born-again Jews are warned that a limping Christian life would cause these unsaved Jews to be turned out of the way. These latter had made a start towards salvation by leaving the temple and making a profession of Messiah. But they needed the encouraging example and testimony of the saved Jews. The words “turned out of the way” are the translation of another medical term, ektrepo “to turn or twist out.”

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Our Daily Bread - Road Builders - The cover of a recent Our Daily Bread pictures a leaf-strewn road through the mountains of Vermont. Those who use the road can enjoy a smooth and beautiful ride over difficult terrain. To make this possible, others had to work hard to chart the route, clear the trees, and level the rough spots.

In a way, all Christians are road builders. We are paving the way of faith for the next generation. The faithfulness of our lives may determine how difficult their journey will be. Will they have to repair the damage we have done to the road? Will they be able to build new roads for others to find the way to God?

To be good road builders, we must heed the advice found in God's Word. The author of Hebrews instructed us to live in peace and be holy (12:14), to make sure no one misses the grace of God, and not to permit a root of bitterness to grow and cause trouble (v.15).

Those of us who have come to Jesus owe gratitude to those who have made "straight paths" for our walk of faith (v.13). In turn, we must remember those who will follow us and make straight paths for them. Let's practice our faith in a way that makes it easy for others to come to Jesus and to follow Him. What kind of road builder are you?—Julie Ackerman Link (Our Daily Bread, Copyright RBC Ministries, Grand Rapids, MI. Reprinted by permission. All rights reserved)

Oh, may all who come behind us find us faithful;
May the fire of our devotion light their way;
May the footprints that we leave lead them to believe,
And the lives we live inspire them to obey. —Mohr
© 1987 Jonathan Mark Music and Birdwing Music

A life lived for God leaves a lasting legacy.