The surname Lax is based upon the German word lachs. Lachs in German means salmon. However, the name Lax was generally just adopted by people in involved in any type of fishing.
Under the "Edikt betreffend die bürgerlichen Verhältnisse der Juden in dem Preußischen Staate" [“Edict Concerning the Civil Status of the Jews in the Prussian State”] on 11th March 1812, Jews in Prussia were given a deadline of 6 months from the publication of the Edict in which to choose a fixed and permanent surname and to declare that to the authority of the place where they were living. Some chose the surname Lax.