The square-root of Siegel modular forms of CHL $Z_N$ orbifolds of type II compactifications are denominator formulae for some Borcherds-Kac-Moody Lie superalgebras for $N=1,2,3,4$. We study the decomposition of these Siegel modular forms in terms of characters of two sub-algebras: one is a $\widehat{sl\left(2\right)}$ and the second is a Borcherds extension of the $\widehat{sl\left(2\right)}$. This is a continuation of our previous work where we studied the case of Siegel modular forms appearing in the context of Umbral moonshine. This situation is more intricate and provides us with a new example (for $N=5$) that did not appear in that case. We restrict our analysis to the first N terms in the expansion as a first attempt at deconstructing the Siegel modular forms and unravelling the structure of potentially new Lie algebras that occur for $N=5,6$.