What is the meaning of "b'Cheik Yutal Es ha'Goral"?
Rashi: A person casts a lot by himself.
R. Yonah: These verses discuss choosing Shalom. First they discuss the praise of ruling over his anger - this Midah pursues Shalom. Now it praises casting a lottery, which suppresses complaints and silences arguments.
Malbim: Some things appear to be given to chance; really, Hashem oversees them. Where man's choice and efforts cease, the eye of Hashgachah appears. E.g. if there is a matter in doubt, and people cast a lottery to know who should receive the matter. Even though the lot is cast b'Cheik, hidden from man's eye and left to chance, Hashgachas Hashem will appear; it is not chance. E.g. the division of Eretz Yisrael was via lottery, with His Hashgachah.
Why does it say "ume'Hashem Kol Mishpato"?
Rashi: Hashem chooses everyone's portion.
R. Yonah: No one should covet his colleague's portion, for everyone gets the portion proper for him that was decreed for him. Some do not like a lottery, even though there is hatred in dividing an inheritance. Some prefer a little in this Avir 1 over much elsewhere. One whose hand overpowers, he wants to choose via force the portion is good in his eyes. Therefore, the verse praises a lottery, to teach about the way of Emunah - what is proper for a person, he will not lose it 2 .