  We show that the dual of every infinite-dimensional Lipschitz-free Banach
space contains an isometric copy of $\ell_\infty$ and that it is often the case
that a Lipschitz-free Banach space contains a $1$-complemented subspace
isometric to $\ell_1$. Even though we do not know whether the latter is true
for every infinite-dimensional Lipschitz-free Banach space, we show that the
space is never rotund.
  Further, in the last section we survey the relations between "isometric
embedding of~$\ell_\infty$ into the dual" and "containing as good copy
of~$\ell_1$ as possible" in a general Banach space.
