I may have found something more or less compatible with your plans, but it will not work if your flight is delayed or if there is an exceptionally long line at incoming passport control. Here it is:

Taxi from airport to Mestre train station.
Train: Mestre 23:17 - Udine 00:53.
Overnight in a hotel in Udine.
Next morning:
Train: Udine 6:35 - Trieste 7:37.
I assume there is no problem hopping over to Lipica from Trieste.
Arrive at the competition in a state of fatigue wich will likely impair your performance.

I would never take the last flight for an important event. Flights do get delayed or canceled... I really feel you should fly in earlier by an extra day. One night in Mestre or Venice. Spend the day in Venice. Next night in Trieste or Lipica. Arrive at the competition in near-optimal shape. If something goes belly-up with the flights, you will probably get rebooked according to your original plan which will become your inconvenient last resort.