A lose battery cable will cause a bad connection so the truck will not start, but will not drain a batter because no amperage is being used.
When you drain the battery by keeping your lights on you hare using up all the battery energy. The truck's alternator is supposed to charge the battery again, but this depends on how long you run the truck. If you only run it for five minutes, you still have drained battery. The amount of gas (engine power) you use does not change the time the battery takes to charge so giving more gas does not help.
It might be that neither the connection or the lights are the problem. Your alternator may be broken. You can't just check this will a meter because an alternator needs to be checked under load and you need a special tester for it.
I would take it to Sears or the dealer and have the alternator checked as well as the battery. They should do the check for free, but ask first.
If the truck is new the battery and alternator will be under warranty so don't buy a new alternator or battery if this is the case. Take it to the dealer if it is a new truck.