This work systematically investigates the charge-transfer dynamics in Li⁺ + K( \rm4s ) collisions from ultralow to moderately low energies, with emphasis on the cross-energy competition between non-radiative and radiative processes. Non-radiative charge-transfer cross sections are calculated over the range of 10^–5–10 keV/u using the QMOCC and TC-AOCC methods. The results show that non-radiative charge transfer is dominated by nonadiabatic coupling between channels. In the collision energy range ( 0.08\;\rm eV/u<E<200\;\rm eV/u), electron capture mainly occurs via rotational coupling into the Li( \rm 2p ) state. As energy increases, multichannel coupling becomes stronger, and the contributions of the 3^2\Sigma^+ and 1^2\Pi channels approach competition. Radiative charge transfer, radiative decay, and radiative association are further studied within 10^–11–20 eV/u using full-quantum, optical potential, and semiclassical methods. When the collision energy is below 0.08\;\mathrmeV/u, radiative processes become dominant. Whenfurther reduced to the ultralow energy region (E<0.01\;\mathrmeV/u), radiative association cross sections are significantly larger than those of radiative charge transfer, indicating a strong tendency for bound molecular ion formation. These results show that nonadiabatic coupling and radiative transitions dominate different reaction pathways in different energy regimes, thereby reshaping the overall charge-transfer dynamics and product distribution. This work provides a coherent physical picture and reliable data for modeling low-temperature ion-atom collisions in plasma physics, astrochemistry, and cold molecular physics. The datasets presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j00213.00247.