  Recent quasi-optimal error estimates for the finite element approximation of
total-variation regularized minimization problems using the Crouzeix--Raviart
finite element require the existence of a Lipschitz continuous dual solution,
which is not generally given. We provide analytic proofs showing that the
Lipschitz continuity of a dual solution is not necessary, in general. Using the
Lipschitz truncation technique, we, in addition, derive error estimates that
depend directly on the Sobolev regularity of a given dual solution.
