For set cover, for a matching, we get $[1/2 - (1-\lambda^\tau) / (1-\lambda) - \tau / (N(1-\lambda))] F^*$.

It's not clear to me if there's a simple interpretation on how to scale $\tau$ with N.

In fact, as @jkbradley pointed out, the $L(1-\lambda^\tau)$ term could possibly be very loose, which makes the approximation guarantee here pretty weak. We should think about tightening this after the NIPS submission.