Does Jehovah Always Determine The "Lot's" Outcome?

I've heard some argue that God always controls the outcome of the "lot" based on Proverbs 16:33. But comparing Proverbs with Joel 3:3 makes me think the verse is being taken out of context:

"and have cast lots for my people, and have given a boy for a prostitute, and sold a girl for wine, that they may drink" (Joel 3:3 WEB).

"The lot is cast into the lap; But the whole disposing thereof is of Jehovah" (Proverbs 16:33 ASV).

Romans 9:18: God Hardens "Whomever He Wills"

Romans 9:18 does not tell us that God hardens all evil humans; it only informs us that "he hardens whomever he wills" (ESV). Jehovah (YHWH) hardens Pharaoh's heart in a sense by permitting circumstances to occur that result in Pharaoh ultimately hardening his own heart (Exodus 7:3-4; 8:11; 9:12; 10:1; 14:4). These points are detailed in Rotherham's Emphasized Bible and Gesenius' Hebrew grammar.

The Complete Word Study: New Testament (by Spiros Zodhiates) makes this observation on Rom. 9:17: "It is not that Pharaoh was 'beyond' the help of God's mercy, nor that God made him wicked, but simply that God withheld his mercy and left him to his own wickedness" (page 522).

Exod. 8:15, 32; 9:34 show that Pharaoh hardened his own heart. See Gen. 3:16ff for an example of God permitting things which the Hebrew Bible says that he causes. Compare 2 Samuel 12:11-12; Jeremiah 8:10.