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πρὸς τὴν Λάχεσιν κτλ. For Lachesis see on 617 C, D, and for δαίμονα 617 D, E notes ἣν -- μοῖραν. In λαχών, ἐφαψάμενον and διεξελθόντα the individual himself is substituted for the soul: cf. IX 573 B. Proclus (l.c. 346. 9 ff.) interprets διεξελθόντα of Er, but this cannot be right. λαχών is said with allusion to Λάχεσις, from whose knees the lots were taken (617 D). It is appropriate that Lachesis should be the only Fate involved in the act of choice; for the Future is the child of the Past (cf. 617 C, D note). The selection is then ratified successively by the Fate of the Present, and the Fate of the Future, and finally, by Necessity herself, the mother of all three. ἀμετάστροφα κτλ. ἀμετάστροφα is said, of course, with reference to the etymological meaning of Ἄτροπος, and ἐπικλωσθέντα in turn alludes to Κλωθώ. In the succeeding clause ἀμεταστρεπτί takes up ἀμετάστροφα again.
The Republic of Plato. James Adam. 1902. Cambridge. Cambridge University Press.
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