Yom Kippur is a special time to atone for sins of illicit relations. It is not for naught that the Torah reading in the Afternoon Services of Yom Kippur is from the section in the Torah portion of Aharei Mot that revolves around illicit relations.
The rectification of the blemish of illicit relations begins with the proper construction of the family unit. Thus, the High Priest must be married, “And he will atone for himself and for his home (his home is his wife)”. Our Torah portion begins “after the death of the two sons of Aaron”. Nadav and Avihu did not marry. They died when they approached the holy place in an unbalanced manner (as we learned in the Torah portion of Shemini). But you, Aaron, may enter, while your wife is waiting for you outside. This rectified situation atones for the Nation. “בְּזֹאת יָבֹא אַהֲרֹן אֶל הַקֹּדֶשׁ"” (“With this [b’zot] Aaron shall come to the holy”). The word for “with this”, b’zot is in feminine form, alluding to the wife of Aaron.
“With this (b’zot) Aaron shall come” alludes to the well-known phrase in Psalms, "בְּזֹאת אֲנִי בוֹטֵחַ"(”In this [b’zot] I will put my trust”), which in turn alludes to the well-known phrase in Proverbs, “בָּטַח בָּהּ לֵב בַּעְלָהּ” (“The heart of her husband trusts in her”). The numerical value of בְּזֹאת אֲנִי בוֹטֵחַ (“In this [b’zot] I will put my trust”) equals, malchut, kingdom. Women are the aspect of malchut. The wife of the High Priest affords him complete trust that Yom Kippur will atone for Israel (according to the Sages, the very day of Yom Kippur atones for evil – even without our own input). All High Priests are referred to as Aaron the Priest and by default, all their wives are referred to as Elisheva, the wife of Aaron. In gematria, the numerical value of אלישבע אשת אהרן כהן גדול (Elisheva the wife of Aharon the High Priest) equals three timesבזאת אני בוטח (In this (b’zot) I will put my trust).”
One of the special ceremonies in the service of Yom Kippur in the Holy Temple is the casting of lots: ”And Aaron shall cast lots upon the two goats: one lot for God and the other lot for the wilderness”. One may think that the outcome of the lottery is by chance. But in truth, it emanates from a very lofty place: the selection made by God. ”"בַּחֵיק יוּטַל אֶת הַגּוֹרָל וּמֵה' כָּל מִשְׁפָּטוֹ (”A person casts a lot close to his own chest, but God decides upon the portion that each person receives.” – Proverbs 16/33). This is the manifestation of God’s selection of the Nation of Israel, whereby all of its sins are cast away to the wilderness.
The lottery also has an essential connection to the rectification of the blemish of illicit relations: Every person has his own lot, and his wife is his lot as ordained in Heaven. ”בחיק יוטל את הגורל” (“A person casts a lot close to his own chest”) alludes to אשת חיקך (your wife who lies close to your chest). Don’t look astray to other places. Rather, remain focused on your own good lot.