To alleviate the issues of low thermal stability and high correlated color temperature, exploring an inorganic color converter with both yellow- and red-emissions to replace the conventional resin/silicone-based phosphor converter for obtaining high-power warm white light-emitting diodes is highly desired. In this study, a series of garnet-based Li₆CaLa_2−2xEu_2xSb₂O₁₂ (x = 0.1–1.0) red phosphors have been successfully synthesized by a conventional high-temperature solid-state method. The microstructure and luminescence properties were systematically investigated by X-ray diffraction, emission/excitation spectra, luminescence lifetimes and temperature-dependent decays. The as-synthesized phosphors exhibited a highly efficient red luminescence at 611 nm corresponding to the ⁵D₀–⁷F₂ electric dipole transition of Eu³⁺, and the luminescence monotonously enhanced as the Eu³⁺ content was increased to 100 mol%. The absence of concentration quenching was ascribed to the large Eu³⁺–Eu³⁺ distance (7.048–7.105 Å) and subsequently the hindering of unwanted energy migration among them in the Li₆CaLa₂Sb₂O₁₂ crystalline lattice. Impressively, the Li₆CaLaEuSb₂O₁₂ phosphor showed an excellent thermal stability with only 9.7% emission loss when the recording temperature was increased from 293 K to 553 K. To evaluate the suitability of Li₆CaLa₂Sb₂O₁₂:Eu³⁺ as a red converter, both the garnet-based Y₃Al₅O₁₂:Ce³⁺ yellow and Li₆CaLa₂Sb₂O₁₂:Eu³⁺ red phosphor co-doped glass ceramics were successfully fabricated by a low-temperature co-sintering technique. Importantly, the adverse energy transfers between Ce³⁺ and Eu³⁺ were efficiently suppressed due to the spatial separation of Ce³⁺ in Y₃Al₅O₁₂ and Eu³⁺ in Li₆CaLa₂Sb₂O₁₂ in the crystal lattice. As a consequence, the quantum yield of the glass ceramic reached as high as 89.3%, and the constructed white light-emitting diode exhibited an optimal luminous efficacy of 101 lm W⁻¹, a correlated color temperature of 5449 K and a color rendering index of 73.7. It is expected that the developed Li₆CaLa_2−2xEu_2xSb₂O₁₂ red phosphors and the related glass ceramics should have potential applications in high-power warm white light-emitting diodes.