The Peter/Petter/Beters of Lauterecken were originally from Elgg, Switzerland, (and formerly Schneit, Kuehlberg, Zurich) and part of a group of emigrants to the Pfalz in the mid 1600s.
You're right; the sources for this branch need improving.
This was from some of my earliest work and obtained in part from a German and Swiss researcher.
I do have Lauterecken parish records, but the ones I have are later, after a female Beter marries into a Wickert/Wichart line about 1691. It's possible that the Beter line in Lauterecken died out.