We were in luck to find a hotel room at the last minute during the busy festival.

were 是 be 动词的过去式复数形式，表示"是"或"处于某种状态"。 in 是介词，表示"处于某种状态或情况中"。 luck 是名词，意思是"运气、好运"。 were in luck 是一个固定短语，字面意思是"处于好运的状态中"，实际表示"很幸运、走运"的意思。