Tereus and Procne. As mentioned (for Itylus) he was killed by his mother: not by accident, however, but deliberately, in order to deprive her husband of an heir (as revenge for his raping of her sister Philomela). Philomela was turned into either a swallow or a nightingale (depending which account one reads) as was Procne, and the song of the nightingale was represented by the Greeks as ity, ity.
This lament was thus Procne (or Philomela) mourning the loss of Itys. His name, therefore, could mean something like 'song of the nightingale'. (There were two Greek words for the nightingale itself, both those of characters in mythology, aedon and philomela: see these as names.)