Yttrium iron garnet (Y3Fe5O12; YIG) has a unique combination of low magnetic damping, high spin-wave conductivity, and insulating properties that make it a highly attractive material for a variety of applications in the fields of magnetics and spintronics. While the room-temperature magnetization dynamics of YIG have been extensively studied, there are limited reports correlating the low-temperature magnetization dynamics to the material structure or growth method. Here we investigate liquid phase epitaxy grown YIG films and their magnetization dynamics at temperatures down to 10 K. We show there is a negligible increase in the ferromagnetic resonance linewidth down to 10 K, which is unique when compared with YIG films grown by other deposition methods. From the broadband ferromagnetic resonance measurements, polarized neutron reflectivity, and scanning transmission electron microscopy, we conclude that these liquid phase epitaxy grown films have negligible rare-earth impurities present, specifically the suppression of Gd diffusion from the Gd3Ga5O12 (GGG) substrate into the Y3Fe5O12 film, and therefore negligible magnetic losses attributed to the slow-relaxation mechanism. Overall, liquid phase epitaxy YIG films have a YIG/GGG interface that is five times sharper and have ten times lower ferromagnetic resonance linewidths below 50 K than comparable YIG films by other deposition methods. Thus, liquid phase epitaxy grown YIG films are ideal for low-temperature experiments/applications that require low magnetic losses, such as quantum transduction and manipulation via magnon coupling.