The need to recover valuable metals from spent lithium-ion batteries (LIBs) is undisputed. However, the environment and the climate are also affected by emissions from the recycling processes. Therefore, the call for environmentally friendly recycling methods is currently louder than ever. In the field of hydrometallurgical recovery of metals from spent LIBs, inorganic acids have so far proved to be an effective, but environmentally problematic, leaching agent, since the pollution of wastewater by high salt loads and the emission of toxic gases cannot be avoided. This has recently led to a trend towards the application of organic acids, as these have significantly more environmentally friendly properties. In order to continue this approach, and to improve it even further from an environmental point of view, this work focuses on the utilization of low leaching temperatures in combination with organic acids for the recovery of valuable metals from spent lithium-ion batteries. This can drastically reduce the required energy demand. Furthermore, attention is paid to higher (50–100 g·L−1) solid-liquid ratios, which are indispensable, especially with regard to the economic establishment of the tested process. The experimental verification of the feasibility using citric, oxalic, and formic acid showed the possibility of an efficient recovery of cobalt, nickel, and lithium. In particular, citric acid in combination with hydrogen peroxide as a reducing agent appears to be a suitable and environmentally friendly alternative to classical inorganic acids, even at low process temperatures, for the hydrometallurgical recycling of lithium-ion batteries.