LACHESIS was the second of the three Fates or Parcae, daughters of Night. She apportioned out the length of human life by spinning the wool from Clotho's distaff (Hesiod, Theogony 214-222; Etym VIII.11.93).
Troilus will die because Lachesis will no longer weave the thread of his life, Tr V.3-7. [Atropos: Parcas]
Lachesis means "the allotting one," Tristia V.x.45-46, and appears in medial position, Tr V.7.