Today's Proverb is not so much about using a system of drawing straws to make a decision, as it is about the sovereignty of God over those decisions. A universal fact of life is that God ultimately has sovereignty over everything that happens. There is nothing that is not under His rule or reign. He takes all things that happen and uses them for His ultimate purposes.
The lot speaks of a system of drawing straws or pieces of wood, with one piece either shorter - or marked in some way to make it distinct from the others. This was one way that difficult decisions were made. It was also a way that God proved to His people that He indeed was sovereign. Take for example the sin of a man named, Achan, in the time of Joshua. Achan chose to take some of the things that were under the ban when they attacked and conquered the city of Jericho. When he did this - he hid what he took in his tent. But his act of disobedience and unfaithfulness caused the Lord to withhold His victory from their next opponent. As Israel wept thinking that God had left them - God said that their real problem was that there was sin in their midst.
God said that He would give a perfect lot to expose who did this. Think for a moment what this meant. There were well over a million to choose from in this lot. It would be impossible for God to show them one man out of a million - by drawing straws. Yet - that is exactly what God did. He did this by breaking Israel down by tribe, group, family, and individual - until God put His divinely sovereign finger directly upon Achan. No less than three different times did God choose one man out of an entire nation - by lot. Oh, and by the way, He was absolutely correct every time. This is no mere game of drawing straws.
What we learn from this is that God is truly sovereign over all things - and from what we read in this particular proverb - all decisions. If we will look to Him in the midst of every decision that we make - we can know He will be the one who guides us. This gives us so much more peace than to think we are at the whims of others - or just in a random world that will only exhibit randomness in every decision. We live in the world guided and directed by the hand of the Omnipotent, Omniscient, Sovereign God, Who knows exactly what He is doing - and where He is going.