The correct order of the events is the following.
1.- In 1759, the British defeat France
2.- In 1814, the British attack Washington D.C. (August)
3.- In 1814, the British lose the battle of Lake Champlain. (September)
4.- The U.S. and British sign the Treaty of Ghent. (December)
5.- In 1815 Americans win the battle of New Orleans.
Here, we are talking about major events of teh War of 1812, another battled confrontation between Great Britain and the United States. Hostilities were supposed to end when both nations signed the Treaty of Ghent on December 24, 1814. Ghent is an important city of Belgium, in Europe. However, the final and decisive battle was the Battle of the port of New Orleans on January 8, 1815. Thi battle was won by the US troops.