This was released by Briggs & Stratton in 2003 edition of Owner's Manual for 422700 series engines (Opposed Twin II).
Needs a bit of update info in that at the time of release, SJ was the latest API classification. The current API classification tops out as SN for gasoline engines.
Some folks like to use oil rated for Diesel engines in their outdoor power air cooled engines because the Diesel lube oil additive package is a little better at protection for surfaces that have high wear potential, such as the camshaft tappets to the camshaft. This area is very hard to maintain ideal lube because the very nature of the shape of a cam lobe presents itself to the tappet almost as a "wiper" (with a concentrated point load) instead of the round bearing shaped surface of the connecting rods.
If you wish to use Diesel engine rated oil, look for API ratings that begin with the letter "C". The latest API classification for Diesel rated oil is CJ-4. Available in single weight or multi-weight configurations.
At the time this was released, API class CF was the highest for Diesel engine oil.

Any good Break in oil with high levels of zinc and phosphorous are good.

30W Lucas Engine Break-In Oil is a very good one.

People forget that engines are test ran at the factory before they are ever shipped out. So unless the re-builder test runs it. Use a break in oil for the first few hours. The high zinc and phosphorous protects the bearings, cam lobes and allows the rings to seat much faster than regular oil.