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Herein, Lu3-x-yCexMnyAl5-ySiyO12 transparent ceramics were prepared via a high-temperature solid-state reaction under a flowing O2 atmosphere and annealed under a H2–N2 atmosphere. The structure and luminescence properties of these ceramics have been discussed in detail. Polished transparent ceramics with uniform grains exhibited the highest optical transmittance of 81.9% at 800 nm. After the introduction of Mn2+ into the ceramic, the photoluminescence (PL) spectrum of the Lu2.885Ce0.015Mn0.1Al4.9Si0.1O12 ceramic showed a green emission band centered at 520 nm and a red emission band centered at 582 nm under the 450 nm excitation. These ceramics exhibited excellent luminescence thermal stability, and the quenching temperature of all the ceramics exceeded 200 °C. The fluorescence lifetime indicated an efficient energy transfer from Ce3+ to Mn2+, and the highest energy transfer efficiency reached 42.3%. According to the PL spectra and emission decay curves, the energy transferred from Ce3+ to Mn2+ via a non-radiative transition. Via controlling the concentration of the Mn2+-Si4+ ions, the emitted light changed from green to orange and the chromaticity color coordinates shifted from (0.3758, 0.5722) to (0.4594, 0.5093). The light-emitting diode (LED) lamps based on Lu3-x-yAl5-yO12 (LuAG):0.015Ce3+, yMn2+, ySi4+ (y = 0.4, 0.6, 0.8) transparent ceramics exhibited low correlated color temperatures (4238–3534 K) with luminous efficacy in the range of 78.52–55.70 lm/W. Thus, the color-tunable Ce, Mn co-doped LuAG transparent ceramics are promising candidates for white LEDs.