"The cast lot puts an end to strife and decides between the mighty ones"
lot
This is the Hebrew word goral, which means a lot or a dice-like multisided cube that was used to decide issues in that day.
There was no idea of luck or chance in the Hebrew mindset. All things that happened to you were decided by the hand of God. You could choose what you would do, but you were only allowed certain choices. Your lot was assigned. If you could improve your lot, then improve it; but if you could not, then it fell to you from the hand of God.
When people did not know what to do, they would throw these dice-like structures to determine what God's will was since God was in charge of even how the lot landed. It was somewhat like our culture uses a coin flip to decide things. The idea here seems to be that when something needs to be decided in which fundamental morality or wisdom is at stake, then since there is no chance – let the lot determine God's will.
We see this technique being used in the New Testament with the picking of a disciple to replace Judas. They had a few men who met the qualifications, and then they cast the lot to see which one would be numbered with the other eleven.
Now clearly this is not advocating using lots for moral and immoral decisions or using lots for wisdom and foolish decisions but suggesting that arbitrary or independent means for assigning equal land (Joshua 18:6), service assignments (Judges 20:9), etc., can be delineated this way. The proverb throws these equal decisions into the hands of God through the use of the lot rather than an endless argument until one is worn down and gives in.
Until tomorrow,
Gil Stieglitz