Why is it called Lions Den Gorge?

I think because the charity foundation of the "Lions" take care of the property and donated the land.

The deep wooded ravine that runs across the northern edge of the property is named Lions Den Gorge and this ravine is what the park is named after.

I don't believe there is a reason for the lions den part. You could always check the signs there for history and context. However the gorge part refers to the large drop off to lake Michigan that the trail runs by.