Lewis & Short

Lȳdĭa, ae, f., = Λυδία, a country in Asia Minor, the capital of which was Sardis, the fabled original land of the Etruscans, Plin. 5, 29, 30, § 110; Varr. R. R. 3, 17, 4; Cic. Fl. 27, 65; Liv. 38, 39, 16 et saep.
Hence,

  1. A. Lȳdĭus, a, um, adj.
    1. 1. Lydian: regna, of Gyges, Tib. 4, 1, 199: aurifer amnis, i. e. Pactolus, id. 3, 3, 29: mitra, Prop. 3, 15 (4, 16), 30: pensa, which Omphale gave to Hercules, Mart. 9, 66, 11: nurus, i. e. Omphale, Sen. Oet. 371: sil. Plin. 33, 13, 56, § 160: lapis, a touchstone (at first found only on the Tmolus), id. 33, 8, 43, § 126: moduli, id. 7, 56, 57, § 204.
        1. (β) Subst.: Lydĭon, i, n., a kind of brick, Plin. 35, 14, 49, § 171.
    2. 2. Transf.
      1. a. Etruscan: Lydius fluvius, i. e. the Tiber, Verg. A. 2, 781: ripa, the right bank of the Tiber, Stat. S. 4, 4, 6: stagna, the Trasimene Lake, Sil. 9, 11.
        (Lydii, false read. for ludii; v. ludius).
      2. b. Rhætian (because the Rhætians were descended from the Etruscans, the descendants of the Lydians): undae, the Lake Benacus, Cat. 31, 13.
  2. B. Lȳdus, a, um, adj., Lydian: Lydus servus, Cic. Fl. 27, 65: puella, i. e. Omphale, Ov. F. 2, 365: Lydae pondera gazae (i. e. aurum Pactoli), Stat. S. 5, 1, 60: nurus, Val. Fl. 4, 369.
    1. 2. Transf., Etrurian, Etruscan.
      As subst.: Lȳdi, ōrum, m.: Lydorum manus, a band of Etruscans, Verg. A. 9, 11.