In Greek mythology, Lycomedes (sometimes Lycurgus) was king of the Dolopians on Scyros. He hid Achilles among his daughters at Thetis' request, fathered Deidamia (and thus grandfathered Neoptolemus), and in Attic tradition pushed the exiled Theseus from a cliff. Distinct from Lycomedes son of Creon.
Adapted from Wikipedia, "Lycomedes" · CC BY-SA 4.0
I.Achilles on Scyros
Foreseeing Achilles' death at Troy, Thetis disguises him as a maiden and entrusts him to Lycomedes. At court Achilles has an intrigue with Deidamia; their son is Pyrrhus, later called Neoptolemus. Odysseus uncovers Achilles (often by a trumpet blast among gifts of arms) and takes him to war; Neoptolemus remains with his grandfather until summoned later.
II.Death of Theseus
Plutarch and Pausanias report that Theseus, driven from Athens, fled to Scyros and was killed by Lycomedes — pushed from a cliff. Motives vary: fear that islanders would make Theseus king, refusal to restore Scyrian estates, or a wish to please Menestheus, who held Athens. The Scyrian king of the Achilles cycle and of Theseus' death is the same traditional figure.
III.Homonym
A separate Lycomedes (son of Creon) appears in other Theban or Argive catalogues. This node is the Scyrian king only (`lycomedes-skyros`), not `lycomedes-creonid`.