The sort of strength we see in the Lion is not that of brute force, it is a sort of inner strength, a mental strength, a will to succeed and strength of character. Thus the lion also symbolises the Will.
A lion is symbolically capable of tackling extremely difficult challenges and succeeding through this inner strength and through their understanding of the need to fight in ways other than direct head to head conflict – so the power of Reason over Emotion.
The Intellect is also the king of the functions, it is the Conscious self and thus rules us.
But, the Intellect is the block to spiritual experience and as such symbolically speaking what we are attempting to do when we are seeking spiritual experience is to ‘tame the lion’.
Left: Here we see this symbolism incorporated in this picture showing the person attempting to find his Higher spirit and become enlightened – shown by the Halo or gold disk, but where his body is being held back by his lion nature.
Right: The same symbolism is incorporated in a number of tarot cards for Strength, where the feminine Subconscious side of our nature tames but does not destroy the male principle of the Conscious side. Notice that it is a male lion being tamed.
The alternative to taming the lion is to ride it symbolically. The meaning is the same, you are taming your Intellect.