They can often be used for each other, but there is a slight difference. If I'm referring to something that was not intentional or planned, I would use either "lead to" or "give rise to". "The little ice age, which started in the 1500's, lead to / gave rise to a change in architecture, with the emphasis on retaining heat." I would use "bring about" if someone or some group was deliberately trying to make some change or have some effect. "The new boss promised to bring about many changes in operations of the department, with the goal of making it more efficient."