It is difficult to mention one faculty who is the most approachable in IIM Lucknow, but Rajiv Kumar Srivastava is one among the rare. 

About Prof. Rajiv Kumar Srivastava:

Qualifications:

• B. Tech. in Mechanical Engineering, Indian Institute of Technology (IIT), Kanpur
• PGDIE (Post Graduate Diploma in Industrial Engineering), NITIE Mumbai
• Ph.D.(IE & OR), Virginia Tech, USA

Research Areas:

He has done his research in Manufacturing and Supply Chain Management in Theory and Practice, IT Applications in Operations Management, pedagogical approaches in Production/Operations Management, and Management Literature.

Recent Research Interest:

• Infrastructural Development by Creating Manufacturing Systems and Enterprise Management Laboratories for teaching/research (through grant-based projects of AICTE/ MHRD) which had resulted in the most comprehensive software for Operation Management in an institution.
• Application of Computer-Based and Analytical Methods in Manufacturing, Indian Context and Best Practices, Enterprise Software Adoption in India, and Developing library collections management.

One of my closest friends attended IIM Lucknow, and Prof. Rajiv Kumar Srivastava used to be his favorite faculty.