In this research, two different hydrometallurgical processes were introduced for recycling the cathodes of lithium-ion batteries (LIBs) from spent LIBs. The cathode materials were leached by malonic acid (MOA), as a leaching agent, and ascorbic acid (AA), as a reducing agent, in the first process, and by l-Glutamic acid (l-Glu), as a leaching agent, and AA, as a reducing agent, in the second process. The results of the tests showed that, with a similar solid-to-liquid (S/L) ratio of 10 g/L and a recovery time of 2 h for both processes, when using MOA of 0.25 M and AA of 0.03 M at 88 °C, 100% lithium (Li), 80% cobalt (Co), 99% nickel (Ni), and 98% manganese (Mn) were extracted, and when using l-Glu of 0.39 M and AA of 0.04 M at 90 °C, 100% Li, 79% Co, 91% Ni, and 92% Mn were extracted. The kinetics of the leaching process for the two systems were well justified by the Avrami equation, which was diffusion-controlled in the MOA + AA system, with the apparent activation energy of 3.23, 14.72, 7.77, and 7.36 kJ/mol for Mn, Ni, Co, and Li, respectively. The l-Glu + AA involved chemical-diffusion kinetic control, with the apparent activation energy for Mn, Ni, Co, and Li of 9.95, 29.42, 20.15, and 16.08 kJ/mol, respectively. Various characterization techniques were used to explain the observed synergistic effect in the l-Glu + AA system, which resulted in reduced acid consumption and enhanced recovery compared to the case of MOA + AA. This occurred because l-Glu is not able to reduce and recover metals without a reductant, while MOA has reductant properties.