  We prove equality of analytic and topological $L^2$-torsion associated with
an odd-dimensional finite volume hyperbolic manifold and a representation of
the fundamental group which extends to the ambient Lie group. This generalizes
a previous result due to L\"uck and Schick. Alternatively, this result can be
regarded as the $L^2$-analogue of recent work by M\"uller and Rochon.
