1. We went on a picnic at Riverside Park.
2. We went on a picnic at the Riverside Park.
(Do you put 'the' before 'Riverside Park'?)
3. The lesson being over, we ran out of the room.
4. Because the lesson was over, we ran out of the room.
5. After the lesson was over, we ran out of the room.
6. When the lesson was over, we ran out of the room.
(What does #3 mean, #4,5 or 6?)
1 is correct. The word "the" is not needed.
3 is very awkward and not used much.
4, 5, and 6 are fine. =)