This matches my records pretty well.You are missing one child of pierre (peter) and amelia LaFayette (fayette) who's name was nelson.I didn't know Lewis had middle name of Peter.
When that family came to Chasm Falls, NY and started having children, all the church records for baptisms, marriages, funerals, etc all have the last name written as (for example) "Peirre Bourcier dit Nicholas" I have the last name like this from dozens of church records.
I have many birth, death, government and religous records plus cemetery stones where even amongst siblings, the siblings may be found using different last name variations: Bourcier, Bushey, Nicholas, and Nicklaw.When looking at the census I have to keep a look out for all those variations.
I didn't see in your note to which of the Bourcier-Nicklaw families you are connected. I have some considerable info on the family in Chasm Falls, NY. If you can contact me maybe we can help eo out.