Yes you are eligible for becoming a lecturer and M.Phil is beneficial in this case.
But now The University Grants Commission (UGC) has made it mandatory even for the M Phil holders to clear the National Eligibility Test (NET) or State- Level Eligibility Test (SLET) before they are considered for the post of lecturer.
For giving NET or SLET exam
You must pass with 55% marks aggregate or equivalent grade at the Master
level in Computer Science/Applications from any recognized University.
If you have completed this criteria you are eligible to take admission in the selected programme from any university.

The Master of Philosophy in Computer Science Program is aimed at developing scholars into researchers, able to make original scientific contributions that have both practical significance and theoretical grounding. The M.Phil. program duration is one year with 2 semesters. The course work includes two Core Papers and two Electives during the first semester.

The Core papers are :
1. General Research Methodology
2. Advanced Computing Techniques

M. Phil scholars in Computer Science perform individual research in any of the areas given below under the direct supervision of an academic expert and submit a dissertation at the end of second semester.

1. Software Engineering
2. Image Processing
3. Data Mining
4. Artificial Intelligence
5. Networks Security
6. Embedded Systems