Typically, a "racing oil" is good for racing engines, NOT street engines, or lawn mower engines.
As we've discussed here before, the valve springs on these old Kohler & Onan engines are so weak they put little load on the cam lobes, so not much zinc is needed to protect the wear surfaces.
I've used the straight 15W-40 Rotella (white jug) in my air cooled engines for close to 19 years with excellent results. I use the 5W-40 synthetic (blue jug) in my other air cooled engine, but it doesn't get near the hours put on it as the one using 15W-40. Per Shell's information line both the T-6 5W-40 & Triple Protection 15W-40 have 1200 PPM of ZDDP, plenty to protect their moving parts. Plus it's easily available at many stores.