Peter Lauer and Marie Remissong had a son named Jean Pierre (John Peter), born May 6th 1876 in Beaufort. His record and the records of some of his descendants can be found at Robert Deltgen's genealogical database: http://www.deltgen.comhttp://www.deltgen.com - Link: Base genealogique publique - by searching for the surname Lauer.
The Civil records of Luxembourg (1796-1890) can be found online at the Familysearch site. The birth record of Marie Remissong is accessible by choosing Beaufort at the list at the left side of the Familysearch page which can be reached via the link http://www.luxroots.com/echttp://www.luxroots.com/ec
Among the Beaufort lists, the births (1800-1854) are in the second list beginning with "Tables de mariage", the title also contains the words "Naissances 1800-1854". The record of Marie Remissong is at Image 1301 (the image number can be put in a specific field). Marie Remissong was born August 4th 1845 in Beaufort (record number 34 of August 5th of the year 1845). Her parents were Jean Remisson (John Remissong) and Marie Lenert. The marriage record of Marie Remissong's parents is at Image 1292 of the title containing the words "Mariages 1803-1863" (record number 18 of December 19th of the year 1843). According to the marriage record, Jean Remisson was born March 22nd 1819 in Beaufort and Marie Lenert was born June 3rd 1819 in Dillingen (municipality of Beaufort).
Berbourg belongs to the municipality of Manternach, so the civil records are accessible by choosing Manternach in the list at the left side, then clicking at the title containing "Naissances 1836-1890" and searching for Image 96. Peter Joseph Emmanuel Lauer was born November 18th 1842 in Manternach (record number 42 of the year 1842).
The next step is to search for the marriage record of Peter Lauer's parents (at the same site).
I can also look for more information about the ancestors of the family in the Parrish books of the 18th century (before 1796) at the National Archives of Luxembourg.