There is no importance of knowing past lives. We move towards the future. No great Master ever spoke about the necessity of knowing past lives for clearing the karma or learning anything.
The learning of karmic lessons is not a mental process nor does it involve our mental ideas of right and wrong. It is a learning of the soul with regard to its growth out of a state of ignorance to a state of knowledge and truth and light which is quite a different thing than a reward and punishment form of learning. Even with reward and punishment it is not so much that a person learns that it is a morally right or wrong thing that he did but rather the whole process of his life that has led him to where he is. For the soul however it is much more than learning. It is an evolution through the hazard of life, its inner and outer challenges towards its full divine potentialities. The law of karma serves the function of keeping each soul on a certain destined track to prevent the hazard of the unpredictable and the unforeseen to become too chaotic. So each soul progresses along certain lines through which it must evolve and encounters certain kind of experiences needed for that. But when we start growing consciously through conscious aspiration, meditation, surrender to the Will of God then the law of karma begins to recede into the background and the true law, the law of Truth begins to unfold carrying us swiftly and relatively smoothly towards the destined goal. The long winding passage through the law of karma changes into a fast forward track so to say.
The knowledge of past lives sometimes spontaneously awakens when we draw near to our soul and unite with it. Then the crucial soul moments of our past lives are glimpsed, not so much as exact and precise details of events and circumstances but as soul-states and soul-scapes against a background of an outer situation whose details may or may not be revealed fully. Thus for example one may remember a few words when one was being martyred or else a moment when one was striding across a battlefield in a warrior mood and recognize in that spontaneous moment that one was such and such a person. But that is besides the point. The important element is the soul-moment when one experienced the pain and the joy of sacrifice or felt a victorious force holding his arms in a war or a luminous being writing through the pen. Of course the memories may be less spectacular (most are like that) or even not very flattering ones such as a king enjoying a life given to pleasure where one has learnt the ephemeral nature of transient joys. This knowledge though may and often does come with an identification with the soul is not really needed for future growth and very often may lead to a certain kind of spiritual romanticism and even become a fertile ground for an imaginative wanderings of the ego in a valley of false glimmers. It is best to stay away from such past life revealers and stick to the course revealed to us by those who have gone before us lighting the way.
Love
Alok da