A fine question. Yes, I definitely think there is a relation between the two. The lion is wounded and in pain, and everyone knows it. It tries to hide its pain, but can't. It comes out all the time, even when it isn't strictly seen. It also ended up where it did due to some fumbling.

The same is true for the couple. Their marriage is wounded, due in part to fumbling, and, while they try to keep up a good front, they are always crying out in pain, pain that eventually becomes literal/physical with the shooting at the end.