la 360 flex plate

The bolt pattern is the same, but the balance weight is different.
Plus, the LA360 uses the standard "daisy" shaped flex plate, the 5.9 uses a full diameter flex plate with a tone ring around the perimeter for the crank sensor. The very early 5.9 plates were non weighted and used a weighted convertor, all subsequent plates had weights and an unweighted convertor.
But as stated, the balance weights are different.