You need a Scroll of Dragon's Lair to access the Dragon's Lair.
The Dragon's Lair is a "dungeon" where you have 3 minutes to buy items (Dragon's Treasure Box (random) boxes) from an NPC for 1 Billion gold each.
You can buy a maximum of 100 boxes in a single 'Buy' click, but you can do so repeatedly until you run out of time or gold.
You can leave with the boxes and open them later.
The Dragon's Lair is located in Rome near the Gate.