LIEs isn't necessarily constructing any new buildings (but if they were, they would have manpower of their own). However, construction work in general does exist in the city and there would probably be jobs for characters who are architects or engineers. A character can find a job in that field as long as it's one that might reasonably exist on Earth. It will be unlikely for a character to be in charge of any major construction project. There are no jobs related to aerospace engineering anywhere in the city.