Plato puts Lachesis at the hinge of the most consequential passage any Greek writer devoted to the Fates. At the close of the Republic, Er reports what he saw in the world of the dead: souls due to be reborn are led before Lachesis, an official casts lots among them to fix the order in which they will choose, and a great array of possible lives is spread on the ground. A herald announces that the responsibility belongs to the chooser and that god is not to blame. Each soul then takes a life, and the order in which it chose determines only how wide the remaining range was, not which life within it.
The adjustment to older Greek assumptions is considerable and Plato makes it deliberately. Lot still governs the sequence, so something outside the person is still at work, but the content of the life is picked by the soul itself, on the basis of the understanding it has brought with it from its previous existence. A soul that lived decently by habit and without reflection is shown grabbing the first splendid tyranny it sees and discovering the horrors packed inside it. Lachesis then gives each soul the guardian spirit that will see the choice carried out, and the thread is confirmed by Clotho and made irreversible by Atropos.
Two things survive that redescription. Allotment remains genuinely binding, and the length of a life remains fixed at the outset by something the person does not control. What changes is where the moral weight sits, and later readers, philosophical and Christian alike, returned to this passage precisely because it lets fate and responsibility occupy the same account without one dissolving the other.