This is one of the first landmarks that pop up when you're looking for info on Lecce, and rightfully so.
The Roman Amphitheatre of Lecce is a well-preserved ancient arena dating back to the 2nd century AD. This amphitheatre, which could seat 15,000 people (some say it was 25,000), once hosted spectacles for the entertainment of the local population. Funny enough, it was only discovered in the early 20th century and is still only partially excavated.
There's a good chance you'll see it's "closed for renovation", but you can practically admire it for free at Piazza Sant'Oronzo! It's extra magical during sunset time (in general, sunsets in Lecce are beautiful).