As the old saying goes, the lion may lie down with the lamb, but the lamb won’t get much sleep.
I understand that P. T. Barnum had a display of a lion actually lying down with a lamb. A reporter asked P.T. how he did it, and P.T. replied "Frequent and judicious application of a lamb".
I saw once on a nature channel where a confused cheetah didn't kill/eat a baby impala because the baby just laid there and didn't run, which would have triggered an attack by the cheetah.