Let X be an abstract set and ℒ a lattice of subsets of X. Some general properties of
Lindelöf, regular as well as normal lattices are investigated for their measure implications and their
relationship to separation properties. Moreover, we show that the generalized Wallman replete
space and the generalized Wallman prime complete space are Lindelöf spaces if and only if certain
measure relationships hold on ℒ.