The Arch Bishop of Canterbury lived in Lambeth's Palace. The grounds overlooked the Thames River in London. The buildings experienced decay and destruction through civil war, and the world wars. However, the palace was rebuilt as a historical monument.
Every year at New Year's the Lambeth Eve celebration occurs in the town of Lambeth. Many people flock to the town and onto the Lambeth Bridge to watch the majestic display of fireworks. While few people actually call it Lambeth Eve anymore, it is a time of celebration as people say goodbye to the past and welcome in the new year to come.
Your question had two parts to it. The first part is that Lambeth Eve is celebrated on the New Year on the Thames River near the Lambeth palace. The second is that Lambeth's Eve falls on December 31, just like the United States New Year's celebration.