I think the replies that focus on the inner state of mind are spot on. I'm surprised no one's mentioned the lemniscate, the infinity symbol. Waite treated it as a representation of the Holy Spirit, which definitely adds a Christianized layer to the card.
Strength, or Fortitude, is about overcoming a challenge, whether physical or metaphysical, through steady endurance. Waite ties it to power, energy, and courage, the classical virtues that help you stand up to threats.
Around 500 A.D. the Roman Catholic Church took the four classical virtues — Strength, Justice, Prudence, Temperance — and added three theological virtues, Faith, Hope, and Charity, making seven total. Early tarot decks echoed that scheme, and decks like the Florentine Minchiate even included all seven.
Fortitude, considered a gift of the Holy Spirit, is often connected with Christian martyrs — think of those stories of people facing lions in the Colosseum. The Androcles and the Lion tale fits nicely: Androcles saves a lion, and later the lion spares him in the arena. Their bond mirrors the garland of flowers linking the woman and the lion on the Strength card.
Whether the lion's mouth is open or closed doesn't really matter — the card reads as trust and affection between them, much like Androcles' lion. Waite's mystical Christianity shaped a lot of his Major Arcana choices, and Strength is no exception.