From the moment Lucas enrolled in the academy, he had already been preparing for the tournament.
If you want to survive in this world, strength isn't the only priority. From ages, there have been many strong people but all of them have fallen into dust.
On top of strength, you need connections and support. And this tournament would be a stepping stone to gain support.
There was no restriction on the artifact and potions in the Tower. You are allowed to take what you want however whether you can use it or not is another matter.
Potions can be carried but the moment you take it, you will be disqualified. Similarly, you can bring what you want but the Tower will restrict its usage if it is deemed dangerous, however, you can stretch and use the loopholes.
In the book, fights had occasionally broken out here and the small passage along walls being cracked and broken was written in the background.