I used Rotella 15w-40 in a Kawasaki FC540V (17hp), and it was too thick. Ended up with glitter in the oil.
15w might be a bit thick in cold temps.
I have always run 10W-30 in my Kawasaki 420V, used it for 2 hours last week in 90 degree weather and the oil temperature taken with an infrared gun was only 213 degrees.
If you keep your mower free of debris, meaning the air cooled passages are clear then I see no need for a thicker oil like 15W-40