My Kliems came from Silesia, a part of Germany that is now in Western Poland. Edward and Adolph (my greatgrandfather) landed in New Orleans in the mid 1850s and settled in Nashville, TN. I have a lot of family data and a few photos I would be glad to share if they are connected. My grandfather spelled his "Lewis" the same as you do, as well as the "Kliem." If you are new to genealogy you would be surprised at how many spelling variations I have found for this surname.
Please reply direct to Iy is quicker that way.
There is another Kliem, in Iowa, who is asking about connections to Texas Kliems.