Summary: A graph \(G\) of even order is \(\ell\)-extendable if it is of order at least \(2\ell+2\), contains a matching of size \(\ell\), and if every such matching is contained in a perfect matching of \(G\). In this paper, we study the extendability of lexicographic products of graphs. We characterize graphs \(G\) and \(H\) such that their lexicographic product is not 1-extendable. We also provide several conditions on the graphs \(G\) and \(H\) under which their lexicographic product is 2-extendable.