I don't know that I have seen a Puritan commentary on the whole of Leviticus. Bonar's is very good but he would not be classed as a Puritan. Calvin might be the closest, although he isn't Puritan either and his Leviticus commentary is part of the Harmony of the Four Last Books of Moses. You will likely have to be satisfied with bits and pieces. I have put all four(!) of the listings from Ralph Martin's, A Guide to the Puritans below:
Gospel Worship by Jeremiah Burroughs deals with Lev 10:3
untitled sacramental sermon by John Owen deals with 16:21, Vol 9:597-599
Two Sermons upon Leviticus by Thomas Manton deals with 19:17, Vol 19:107-124
Festival Kept to the Lord by Edward Payson (not really Puritan) deal with 23:39, Vol 2:275-292
If you can get a hold of Joseph Caryl's, Practical Observations on Job set there are over 30 references to Leviticus in the index but they would likely all be very brief; perhaps just a mention in a sentence.
Wayne has a good resource above and I would recommend taking advantage of it. Even though, strictly speaking, Spurgeon is not classed as a Puritan either he would be quite helpful and "Puritan-like". The only Puritan resources I have seen are Manton, Owen & Burroughs with Burroughs being the largest albeit on a limited section of Leviticus.
Another good resource would be the Jamison, Fausset & Brown commentary. Although, again not Puritan, it will be helpful. The best, In my humble opinion, modern Leviticus commentary is the one by Gordon Wenham in the NICOT series. He does an excellent job of connecting Leviticus with the New Testament.
If anyone has any other Puritan suggestions on Leviticus, I am all ears and would like to hear suggestions myself.