Question: Is it so that those who have fallen into one of the three lower realms will have to be reborn in all three before they can exit from them?
Answer: It depends on where they fell to in the first place. (Note that from bottom up, from the worst to the ‘better’ of the three lower realms, the sequence is the realm of hell-beings, hungry ghosts and animals.)
Typically, if in the hell realm, there will be rebirth there a number of times, with gradual ascent up to the hungry ghost realm. If in the hungry ghost realm, there will be rebirth there a number of times, with gradual ascent up to the animal realm. If in the animal realm, there will be rebirth there a number of times, with gradual ascent up the human realm.
This is so as when negative karma lessens, there is ‘upgrading’ to the immediate ‘better’ realm accordingly. If say, a human is reborn as an animal, unless this animal creates worse karma in that life, this being should not fall lower to be a hungry ghost or hell-being – or it would be karmically ‘unfair’.
Rebirth in each of the lower realms is usually for a long time and for a large number of times. Hell-beings are repeatedly ‘revived’ after death to suffer, due to much hellish karma to expend. Hungry ghosts can have long unfortunate lives. Animals, if as insects, for example, can be reborn so for hundreds of times. This is so as their lives are short, while there is much animal karma. However, these ‘sequences’ and durations are only in general, not so if there are adequate merits and guidance received, to make bigger ‘leaps’.
An example is that of Mahamaudgalyāyana rescuing his Mother, from the hungry ghost realm, immediately to a human or heavenly realm: thedailyenlightenment.com/2019/01/how-to-help-the-deceased-with-the-triple-gem There are also cases of hell-beings, hungry ghosts and animals ‘leaping’ to Pure Land directly (which is the other end of the ‘spectrum’ of existence) – when they give rise to the Three Provisions of Faith, Aspiration and Practice: purelanders.com/2018/02/08/the-three-provisions.