Yes, you can prepare for GATE while doing an M.Tech from IET Lucknow. You will have to self study and make a schedule that works for you. There are GATE coaching centers near IET. If you opt for hostel accommodation, you can easily manage your coursework and preparation for GATE.
M.Tech in the Mizoram university is very new and will take a bit to settle, so the placement is not quite good.
The students collaborate with NIT Mizoram students to send the companies so that the process of placement could be completed. But the package they offer is not at all satisfying for the students.
The Department of Electronics and Communication Engineering has started M.Tech. and Ph.D. Programme from academic session 2017-18. Along with this 2 more M.Tech. programmes in Computer Science and Engineering, Power and Energy Systems Engineering; Ph.D. programme in Electrical Engineering started their academic sessions from the year 2018-19.
The placements will take time to improve but currently it is average, so if you prefer self learning and training only then opt for MZU, otherwise go for more experienced colleges.
IIT Hyderabad is one of the recognised academic institutions in the country.