We investigate the relation between anisotropic finite-field phase boundaries, low-temperature entropy accumulation, and adiabatic demagnetization in Li${}_6$Gd(BO${}_3$)${}_3$, a large-spin Gd${}^{3+}$ magnet with a structurally quasi-one-dimensional zigzag-chain motif. Magnetization, heat-capacity, and field-down magnetocaloric effect (MCE) measurements for $B\parallel c$ and $B\parallel b$ are complemented by direct demagnetization of a 20.15~g single crystal for $B\parallel b$. In zero field, a $\lambda$-type heat-capacity anomaly marks long-range order at $T_N\approx 0.6$~K, but only about $0.39Rln8$ of the entropy is released by $T_N$, consistent with substantial short-range correlations above the transition. For $B\parallel c$, the phase boundary extrapolates to a zero-temperature field scale near 1.45~T, whereas for $B\parallel b$ two boundaries near 0.4 and 0.8~T enclose an intermediate phase whose spin structure remains unresolved. Classical Monte Carlo simulations of a minimal quasi-one-dimensional $J$ XXZ chain model reproduce the $B\parallel c$ field scale semiquantitatively. Enhanced low-temperature entropy and extrema of the MCE-derived magnetic Gr"uneisen parameter ${\Gamma }_B^{MCE}$ occur near these phase boundaries. Isentropic estimates from 6~T and 1.8~K give terminal temperatures of about 150~mK at 1.45~T for $B\parallel c$ and 108~mK at 0.4~T for $B\parallel b$. Direct demagnetization from 8~T and 1.9~K reaches about 155~mK and resolves cooling minima near both 0.8 and 0.4~T, indicating that the field-dependent distribution of low-temperature magnetic entropy, rather than the zero-field limit alone, governs the optimal demagnetization trajectory.