We give a sufficient condition for exponential stability of a network of lossless telegrapher's equations, coupled by linear time-varying boundary conditions. The sufficient conditions is in terms of dissipativity of the couplings, which is natural, for instance, in the context of microwave circuits. Exponential stability is with respect to any $L^p$-norm, $1\leq p\leq\infty$. This also yields a sufficient condition for exponential stability to a special class of systems of linear time-varying difference-delay equations which is quite explicit and tractable. One ingredient of the proof is that $L^p$ exponential stability for such difference-delay systems is independent of $p$, thereby proving again in a simpler way some results from [Y. Chitour, G. Mazanti, and M. Sigalotti, Netw. Heterog. Media, 11 (2016), pp. 563--601].