An L-filter base, L-filter, L-ultrafilter is a filter base, filter, ultrafilter consisting exclusively of Lindelöf sets. In this paper we consider L-filters (ultrafilters) and LC-property. A space X is LC − space if every Lindelöf set in X has the compact closure in X. A locally compact space X is LC − space if and only if every L-ultrafilter on X converges. We also consider L-points, L-sets and LC-extensions.