[1] Taken from Timaeus' Platonic Lexicon s.v., and repeated in other lexica: see the references at Photius kappa663 Theodoridis, noting the nineteenth-century (Baiter-Sauppe, Naber) attribution of the headword participle to Plato, Menexenus 235A; see further below.
[2] The verb khle/w means to beguile, particularly with music, though not exclusively by pipes (LSJ s.v. and kappa 1515). The present middle/passive participle is first attested in Euripides fr. 10.87 Page, but the likely source for the lexica is Plato, consistent with Timaeus' gloss. Besides Mexenenus 235B (by orators -- the cited masculine nominative singular), above, see also Laws 885D (charmed by gifts -- nominative plural), Republic 607D (by poetry -- dative plural) Phaedrus 259A (by the sound of cicadas -- accusative plural). Timaeus' pipes are illustrative and not defining for the verb, as the Suda implies in its extrapolation, since Plato does not directly refer to them.