I can see from the RtL rules that if a lieutenant ends movement on a space with the heroes, he may attack them. Likewise, if the heroes end movement in a space with a lieutenant, they may attack him. However, I could find nothing in the rules about attacking when starting in a shared space.
If the heroes start their turn in a city, and there is also a lieutenant at that city, can they attack him? If they can, do they get to do any training in the city after finishing the fight, or does it take up their whole game week. Likewise, if a lieutenant starts his activation in a city where the heroes are, can he attack them without moving, and if so, would he still be able to put down a siege token there during the same turn?