Let F be a free Lie algebra of rank> 1 and S be an ideal of F. Denote by Fmand Fnl,…,nkthe terms of the lower central and the polycentral series of F. The aim of this paper is to provide a sufficient condition for the quotient algebra Fnl,…,nk/Snl,…,nkto be infinitely generated. The case Fm/Smwas studied in [6] for free groups and in [ 2 ] for free Lie algebras. In this paper the following main theorem is proved : If F = F2 = S, k > 1 and ni> 1 for i=l,…, k, then Fnl…,nk/Snlis infinitely generated.