A continuous, hot vapor stripping process recovers base oil from used lubricating oils (ULO) containing lubricating oil boiling range material, with further refining using solvent extraction to produce a high quality base oil. The ULO is charged to a first stripping column along with a stripping vapor to vaporize lubricating oil boiling range components, which are fed to a second stripping column to separate diesel boiling range material from the lubricating oil boiling range components. A lubricating boiling range material is removed as a bottoms product and fed to a liquid-liquid extractor to produce a raffinate stream and an extract stream. The raffinate stream is fed to a raffinate distillation column, where a base oil product is recovered as a bottoms stream. The extract stream is fed to an extract distillation column, where an aromatic oil product is recovered as a bottoms stream.