Why Italy did not find Illustrious after launch

Did Italy determine the attackers' launch direction and send aircraft after Illustrious?

No. Italian forces barely knew where Illustrious was and did not mount a meaningful counterstrike against her.

Italian defenders did not infer the Swordfish launch direction accurately enough to find Illustrious. They barely knew the carrier's position and mounted no substantial strike against her. Carrier mobility and the wider operational deception complicated the search. Limited radio emissions also reduced the clues available after launch.