Yes.
Most of the Lube oils generally get oxidised in use. Unless used oils are mixed-up with other oils and or get emulsified or contaminated in storage, they can be suitably re refined.
During modern re refining process, referred to as a combination of Thin Film Evaporation and Vacuum Distillation the used oils, undergo a multiple stage operation.
1. Dehydration
2. Diesel stripping
3. Vacuum Distillation.
4. Hydrofinishing.
In comparison, base oil from Crude Oil refining, would have already passed through multiple fractional distillation, as it is an intermediate process. In summary, the process involves:
1. Fractional Distillation
2. Solvent extraction
3, Hydrofinishing
Used oil is often further treated by a Filteration / Clarifying process to improve colour and smell. The end result is a re-refined Base Oil that makes it at par, with fresh Group I Base Oils.