The name Tyrsenus appears elsewhere as a variant of Tyrrhenus whom many accounts bring from Lydia to settle the Tyrsenoi/Tyrrhenians/Etruscans in Italy.
Dionysius of Halicarnassus (1.28.1) indeed does cite a tradition that the supposed founder of the Etruscan settlements was Tyrrhenus the son of Heracles by Omphale the Lydian who drove out the Pelasgians of Italy from the cities north of the Tiber river.
Strabo (5.2.2) makes Atys father of Lydus and Tyrrhenus to be one of the descendants of Heracles and Omphale.