The problem was that there is a scene with Lise the game was supposed to trigger once she reaches lv 4 to learn the first ice spell. I'm not sure if it's due to a bug on the version you played, but that scene didn't play. I confirmed that in order to fix your save, you just need get enough exp to Lise to level up, make sure your game version is at least v1.07 which is the version I tested in, then sleep at the city inn so she levels up. This should trigger the event right before the one you need. Once that's done, sleep at the same inn again and yet another cutscene should trigger and this time giving the flower accessory in your inventory back and chaining to the string of events leading to the arena.
I'll attach a savedata folder with new saves on location 15 and 16. 15 has Lise levelled up once and triggered the event right before giving the hair accessory. Just need to sleep at the inn once more with Lise. 16 has arena unlocked and you just need to wait until Sunday for the arena to open.