We assess the capabilities of the LiteBIRD mission to map the hot gas distribution in the Universe through the thermal Sunyaev-Zeldovich (SZ) effect. Our analysis relies on comprehensive simulations incorporating various sources of Galactic and extragalactic foreground emission, while accounting for the specific instrumental characteristics of the LiteBIRD mission, such as detector sensitivities, frequency-dependent beam convolution, inhomogeneous sky scanning, and 1/f noise. We implement a tailored component-separation pipeline to map the thermal SZ Compton y-parameter over 98% of the sky. Despite lower angular resolution for galaxy cluster science, LiteBIRD provides full-sky coverage and, compared to the Planck satellite, enhanced sensitivity, as well as more frequency bands to enable the construction of an all-sky thermal SZ y-map, with reduced foreground contamination at large and intermediate angular scales. By combining LiteBIRD and Planck channels in the component-separation pipeline, we also obtain an optimal y-map that leverages the advantages of both experiments, with the higher angular resolution of the Planck channels enabling the recovery of compact clusters beyond the LiteBIRD beam limitations, and the numerous sensitive LiteBIRD channels further mitigating foregrounds. The added value of LiteBIRD is highlighted through the examination of maps, power spectra, and one-point statistics of the various sky components. After component separation, the 1/f noise from LiteBIRD's intensity channels is effectively mitigated below the level of the thermal SZ signal at all multipoles. Cosmological constraints on S 8 = σ 8 (Ωm /0.3)0.5 obtained from the LiteBIRD-Planck combined y-map power spectrum exhibits a 15 % reduction in uncertainty compared to constraints derived from Planck alone. This improvement can be attributed to the increased portion of uncontaminated sky available in the LiteBIRD-Planck combined y-map.