I'd like to read the answer as well!
Because Diesel oil and lube oil differ only by their molecular weight, don't they? And they even dissolve another.
So would some solvent act specifically on Diesel and not lube, or the opposite? Or can they be separated only by distillation, as they have been when produced from crude oil?
Also: lube oil uses to contain additives. While heavy fractions of crude oil naturally make good lubricants, additives make the high quality lubricants, with viscosity constant over temperature, with corrosion protection, and the like... What should happen to these additives during the separation with a solvent?