The LDS Gospel Doctrine lessons skip right over Leviticus, but I thought I'd see what I could put together anyway. See my Leviticus article.
The material in Leviticus was revealed about a year after Moses led the Israelites into the wilderness. This could be anywhere from as early as about 1550 BC to as late as 1220 BC, as I've documented in previous posts.
In my Patriarchs Timeline I guesstimated the start of the Exodus as 1552 BC. In my article about the strange ages of the four Patriarchs, I guessed 1491 BC.
One guess is as good as another. Don Fortner has 1490 BC, and Chuck Swindoll and Frank DeCanio both have 1446 BC, just to give a few you can look up for yourself.
The Old Testament Student Manual doesn't really pin down any date, but suggests some possible synchronisms with known Egyptian rulers. It favors a later date rather than an earlier one, and mentions 1220 BC as a date when the "Habiru" were already in Canaan. But they could have arrived much earlier.
It took a long time to format all the chiasms in Leviticus that I found online. If you want to see a really ambitious approach to Leviticus, see Chaver. Someone please explain it to me.
In retrospect, a lot of the chiasms in my two Exodus articles might have been the result of people looking for patterns where there really are none. What do you think?
You are expecting me to remind you to read your Book of Mormon, but I've decided not to say anything about that in this post.