  We show that every Lorentz sequence space $d(\textbf{w},p)$ admits a
1-complemented subspace $Y$ distinct from $\ell_p$ and containing no isomorph
of $d(\textbf{w},p)$. In the general case, this is only the second nontrivial
complemented subspace in $d(\textbf{w},p)$ yet known. We also give an explicit
representation of $Y$ in the special case
$\textbf{w}=(n^{-\theta})_{n=1}^\infty$ ($0<\theta<1$) as the $\ell_p$-sum of
finite-dimensional copies of $d(\textbf{w},p)$. As an application, we find a
sixth distinct element in the lattice of closed ideals of
$\mathcal{L}(d(\textbf{w},p))$, of which only five were previously known in the
general case.
