Don't know if this helps you at all, Tom.
Sourced from the Learn/Family Facts/Name meanings on ancestry.com.
Lyman. "Americanized form of German Leimann, Americanized form of Leinemann, habitational name for someone from Leine in Pomerania, or for someone who lived by either of two rivers called Leine, near Hannover and in Saxony."
About the closest reference I can find mentioning a GERMAN origin for the name. You have to understand that Prussia encompassed a large area of Northern Germany prior to WW1.