“lap.” The “lap” actually refers to the fold, or “pocket” made in the garment that is about where the lap is. People wore long outer garments and tied them up by a belt or sash, and it was common to tie the garment in such a way that it had a pocket where different things, for example money, could be put. The “lot” was usually actually at least a couple, and sometimes more, stones or items that were different but felt the same to the hand. In making decisions, the stones would be “cast” (or placed) into the pocket and then one drawn out that would make the decision. The High Priest set a great example for this, because he had the Urim and Thummim inside a pocket in his breastplate that were used in making decisions (cp. Exod. 28:30; Lev. 8:8; Num. 27:21; Deut. 33:8; Ezra 2:63; Neh. 7:65).
To understand this Proverb correctly, we must understand that it is written from the greater perspective of Proverbs, which is that the one casting the lot is a righteous person with good intent, so God can help with making the decision. This verse is not a “stand alone,” apart from the scope of Proverbs; it is not saying that any chance throw of the dice is God’s decision. The way a lot, or dice, or other forms of divination work, the result can be by chance, from God, or influenced by Satan and demons.
We see Satan involved in divination all the time; in fact, many ungodly forms of decision-making, including casting lots for ungodly purposes, were influenced by invisible demonic forces. The ancients believed that invisible spiritual powers guided the “lot” or other means of divination, and they were certainly correct in that. Thus, what looked like chance was actually controlled by spirits, or God. In fact, witches and people involved with the occult have used divination for millennia because it is a good way that Satan can be involved in decision-making without having to come out into the open. So, for example, the wicked Haman cast lots to pick a date to destroy the Jews (Esther 3:7).