The big cities (Lahore, Karachi) never sleeps in night especially during summer. There are lots of spot in Lahore where you can go any time during night. The famous Food Street, the Lakshmi Chowk, Anarkali, Ichhra, Bhaati and Lohari gate are all open for almost whole night and offer delicious food of every kind.
Every kind of transport (van, rikshaw) is also available till late night.
You can also try theaters of Lahore (Alhamra, Tamaseel, Open air, and many more) or cinema as well.
Lahore has a red light area known as 'shahi mohallah' (behnd the Lahore Fort, inside the walled city). But if you are stranger never go there alone rather go with some local person.
Yes, Pakistan does have some kind of nightlife. This cafe is the meeting point for rich and beautiful young Lahoris and you will even see girls in tight dresses smoking cigarettes. Just like at home, except for one thing : even here they don't sell alcohol.
The music mix here is fun : Beatles, J.Lo and even the Gipsy Kings!
Dress Code: If you're a westerner it doesn't matter what you're wearing. But it would be respectful to dress up a bit, unless you want to be a misfit.