Apparatuses and processes for producing at least one lubricant base oil and at least one hydrocarbon fuel range product. A deasphalted oil and a VGO stream and passed to a first hydroprocessing zone. After the first hydroprocessing zone, the hydrocarbon fuel range product may be recovered. After recovering the hydrocarbon fuel range product, the unconverted material may be separated into one or more lubricant base oil streams, and a recycle stream. The lubricant base oil streams may be upgraded, while the recycle stream may be hydroprocessed in a second hydroprocessing zone. The effluents can be combined to allow for efficient separation and recovery of the desired products.