Summary: We show that the generating function of electrically charged \( \frac{1}{2} \)-BPS states in \( \mathcal{N} = 4 \) supersymmetric CHL \(\mathbb{Z}_N\)-orbifolds of the heterotic string on \(T^{6}\) are given by multiplicative \(\eta\)-products. The \(\eta\)-products are determined by the cycle shape of the corresponding symplectic involution in the dual type II picture. This enables us to complete the construction of the genus-two Siegel modular forms due to J. R. David, D. P. Jatkar and A. Sen [J. High Energy Phys. 2007, No. 01, Paper No. 016, 31 p. (2007), arxiv:hep-th/0609109] for \( \mathbb{Z}_N \)-orbifolds when \(N\) is non-prime. We study the \( {\mathbb{Z}_4} \) CHL orbifold in detail and show that the associated Siegel modular forms, \( \Phi_{3}\left( \mathbb{Z} \right) \) and \( \widetilde{\Phi_3}\left( \mathbb{Z} \right) \), are given by the square of the product of three even genus-two theta constants. Extending work by us as well as by M. C. N. Cheng and A. Dabholkar [Commun. Number Theory Phys. 3, No. 1, 59–110 (2009; Zbl 1172.81015)], we show that the ‘square roots’ of the two Siegel modular forms appear as the denominator formulae of two distinct Borcherds-Kac-Moody (BKM) Lie superalgebras. The BKM Lie superalgebra associated with the generating function of \( \frac{1}{4} \) -BPS states, i.e., \( \widetilde{\Phi_3}\left( \mathbb{Z} \right) \) has a parabolic root system with a lightlike Weyl vector and the walls of its fundamental Weyl chamber are mapped to the walls of marginal stability of the \( \frac{1}{4} \) -BPS states.