The soul itself is the determiner in matters of reincarnation, not any "lord" or other being. Such information about the "Lords of Karma" as you related that you discovered is fear-based and full of error. In other words, the reason it is full of error is because
it is fear-based, for anything that is fear-based is thus heavily distorted.
Such unending cycles of misery do not exist, nor can they exist. Evolution of consciousness is part of the cosmic drama that we are living, and no such fate could ever befall a soul that it would endlessly repeat an action or same type of pattern. There ARE occurrences where people--based upon their particular strong religious beliefs in such beings--manifest "Lords of Karma" that await them after they depart the physical plane, as this is indeed part of the religious cosmology of some regions and eras in human history, yet these are but astral projections of consciousness, and at all times it is the soul that is the true lord of its incarnations.
There are indeed loving beings
who help people "burn off" their karmic ribbons, so to speak, and these may be seen as the true Lords of Karma, or even as "angels," yet these beings--as ALL beings in creation--can only assist, they cannot control nor manipulate another's karma
for them. However, the Higher Self actually fulfills this function (as well as other functions), so in this sense all people have their own personal "Lord of Karma" that is their own higher consciousness.
The "Lords of Karma" information that is fear-based is nonsense, it is rubbish that has no real place in the universe except as a low-level fantasy that is created out of an imagined need for a type of divine "judge, jury and executioner." This type of heavily distorted information is directly related to the type of consciousness that imagined "Jehovah" as an angry father-figure who punishes people, and it is the same type of mind that created gods such as "Zeus."
You need not be concerned with such silly gods and "lords," for these do not represent the True Nature of the Divine Source, which is infinitely loving and blissful beyond description.
Thank you for posing such an interesting topic. Best Wishes, I extend you.