The Lich will appear once you've placed a certain number of 'tiles' on the map. This includes all types of tiles: Road, Roadside, and Landscape. The exact number varies slightly but generally occurs after around 10-15 tiles have been placed. The Lich's Palace will appear on the campfire tile, and he will engage you on the next loop.
Before summoning the Lich, ensure your hero is well-equipped with the best possible gear. Try to have a few potions saved up. Consider placing a Vampire Mansion near the campfire for extra healing before the fight, or a Blood Grove to finish off low-HP enemies quickly.