"Decided to do X the next time she went for a walk" vs. "...the next time she goes for a walk"

In terms of time, it's not necessarily in the future.

It's in the future-of-the-past. The event of the lion next going for a walk is an event that can take place any time between the past event of her making that decision, and what is still the future. It could be tomorrow, but if the lion decided this last week, then that walk could have been yesterday.

Since the superordinate clause is in the past tense, backshifting can bring the subordinate into the past too.

On the other hand, if we we had that clause in the present tense:

The lion with a thorn in her paw decided to wear sneakers the next time she goes for a walk in the jungle.

That suggests that this walk is asserted to still in the future. Backshifting isn't required for a statement about the present or future that still holds.

The sentence is reporting the decision by the lion.

As the decision to wear sneakers the next time she goes for a walk is in the past, it is reported by backshifting the verbs - she decided to wear sneakers the next time she went for a walk.

To backshift verbs:

Simple present > Simple past
Present Perfect > Past Perfect
Simple Past > Past Perfect