What does the Lehmkuhl name mean?

The family name Lehmkuhl consists of the combination of two German words, "lehm" and "kuhl" or "kühl", which likely referred to the place or occupation of the original name bearers.
The German word "lehm" means clay^[01], sticky muddy soil good for making bricks, pots, etc. "Kuhl" (without the umlaut)comes from the Middle Low German word "kule", meaning mine, pit or hole^[02] from where the clay could have been mined; Whilst "kühl", with the umlaut, means cool or cold^[03].
Thus the original bearer(s) of the name has either lived near mines or has worked as miners themselves. A literal translation of the family name Lehmkuhl, without the umlaut, could then be "clay miners" or "those that live near clay mines". Lehmkühl, with the umlaut, could refer to someone that has perfected the cooling technique for finished clay products.

Dictionary of American Family Names, Oxford University Press, ISBN 0-19-508137-4:

1. North German: topographic or occupational name for someone working or living by a clay pit, from Middle Low German lem 'clay' + kule 'pit', habitational name from any of several places named with this term, for example Lehmkuhlen near Kiel.
2. South German version is Leimkuehler.