Just FYI, there is also a Matthias Lauterbach born 28 Nov 1754 in Pilesgrove, Salem Co., NJ. He was the son of Conrad Lauterbach, who came to the US with his brother Peter in 1737. Both men settled in Salem County, NJ by the mid 1740s. Conrad married Elisabeth Jonsson.
Matthias served in the RW with his twin brother, Adam and another brother Conrad. Matthias died sometime after 1797.
Matthias married Ann Curry in 1776 in Swedesboro, NJ and they had nine children. One of their daughters married Jesse Avis/Avise and moved to Illinois.