It is both the academic's and the institution's responsibility. The lecturer focuses on the pedagogical aspects, discipline knowledge and capabilities. The institution oversees the quality of the curriculum and the standards. The institution has a responsibility to protect the student's investment and ensure that it graduates students with the skills promised on enrolment.
If you are the professor, own the lecture. You are responsible to see that your material is the most current. If only because you are presenting yourself as the authority to the students. It is your responsibility to stay current otherwise we are just parrots repeating what we have heard from the institution. If the institution provides or mandates all of the material, then why do they need me. Let them give the lecture.
1. Updating curriculum is a broad activity and neither Lecturer nor educational institutional alone do the work!
2. It is a holistic activity which might emanates within lecturer's vision and understanding and go beyond to other stakeholders including the students, employers, accreditation agencies, faculty with the same disciplines, on-going students' alumni networks, the industry, authorities etc.
For a concerned question: Both lecturer and educational institutions play equal part.
Updating curriculum is neither the responsibility of the instructor nor the educational institutions. In our country, it is the responsibility of the Ministry where a committee holds regular meetings to review the curricula each four or five years. The teacher may modify or moderate certain aspects but within the limits of her/his authority just to meet the needs of their students. Drastic changes are the total responsibility of the relevant Ministry.
It is basically the job of the Institution, since there may be different lecturers teaching the same in different classes and the evaluation is centralized at college or university level. The lecturer has to recommend about what updation in his view are required, as also update his own teaching notes & lectures and not re-run the same stuff every year.
It's the core responsibility of the Ministry of Education via the educational institution but the inputs of the updated curriculum is the duty of lecturers who teach the course. They often suggest the updates, the areas of the curriculum that need the updates etc. Afterall, they are the final implementers of the policy in the classroom.