Need advice to improve low-light focusing technique

I'm by no means an expert, but I have the 70-300 and I suspect that some significant portion of the softness is just a characteristic of the lens at that aperture.

It's not clear what the distance is to the lion, but also consider that you're an hour past sunset, in September, so I'm guessing the ground is warmer now than the air immediately above it, so it's radiating heat into the the air, causing minor eddy currents in the air that can also distort an image. (Would also be useful to know if there were any significant differences in terrain over the intervening distance. If you're shooting over a stream or a road, or even grass versus bare dirt or something, there's an even greater likelihood of an unstable air mass you're shooting through. Upon reflection, I'm going to say that this probably accounts for most of the softness, with the rest being just the limitations of the lens at that aperture and focal length.)

Combine that with 1/60th shutter speed (a rather long exposure even with IS at that focal length), 3200 ISO (very clean, but not perfect) and I think you have most of your explanation.

Suspect focus worked just fine.

But again, I'm not an expert. I'll be interested to hear others' thoughts.