How do I convert this simple Laplace equation to Z-domain?
I believe, mike, that the answer to your question is likely the Bilinear Transform.  Make sure you identify the significant frequency (likely the resonant frequency of the LPF1 and LPF2 or $H_b(s)$ and apply prewarping to that frequency, so that the digital filter hits at the same place that the analog filter.  Remember the transfer functions of the two delay lines are $z^{-N_1}$ and $z^{-N_2}$.  Or, in the s-domain $e^{-N_1sT}$ and $e^{-N_2sT}$ , where $T$ is the sampling period or the reciprocal of the sample rate.