The high specific capacity of Li-ion batteries requires a high Li ratio anode. However, a high Li ratio indicates the structure of the anode compound is complicated. For compounds with similar elements, a more complicated crystal structure usually means a lower thermal transport property based on the classical Slack model, i.e., the thermal conductivity of crystals is negatively correlated with the number of atoms in primitive cells, which inevitably increases the risk of thermal runaway and seriously hinders the widespread use of Li-ion batteries. In this study, however, our machine-learning-potential-based atomistic simulations show that the room temperature thermal transport capacity of a possible complicated anode candidate $\mathrm{L}{\mathrm{i}}_{15}\mathrm{S}{\mathrm{i}}_{4}$ (i.e., $\ensuremath{\sim}3.0$ W/m/K and a theoretical capacity of 1857.26 mAh/g) is comparable to that of the traditional anode LiSi (i.e., $\ensuremath{\sim}3.28$ W/m/K and a theoretical capacity of 765.1 mAh/g). Our spectral analysis shows that the increase of the Li ratio will generate many optical branches with frequencies higher than 4 THz and largely decrease the specific heat of vibrations below 4 THz. Meanwhile, these vibrations with frequencies lower than (above) 4 THz are found to mainly transfer thermal energy through propagating (both propagating and coherence) channels. The thermal conductivity contributed from vibrations with frequencies lower than 4 THz decreases from 2.54 W/mK for LiSi to1.99 W/mK for $\mathrm{L}{\mathrm{i}}_{15}\mathrm{S}{\mathrm{i}}_{4}$. However, the smaller frequency difference among vibrations with frequencies above 4 THz in $\mathrm{L}{\mathrm{i}}_{15}\mathrm{S}{\mathrm{i}}_{4}$ are found to increase the thermal transport capacities of these vibrations via the overwhelming coherence channel compared to the propagating channel. The thermal conductivity contributed from these vibrations is 1.01 W/mK for $\mathrm{L}{\mathrm{i}}_{15}\mathrm{S}{\mathrm{i}}_{4}$ and 0.74 W/mK for LiSi. As a result, $\mathrm{L}{\mathrm{i}}_{15}\mathrm{S}{\mathrm{i}}_{4}$ with a complicated crystal structure possesses a similar thermal transport capacity compared to the simple crystal LiSi.