What are the college timings like at NLSIU and NALSAR? Can you keep your regular job while studying here - at least for the first 2 years?

The subjects offered at both institutes are full-time courses. NALSAR and NLSIU are both premier educational institutes of the country that offer professional law degrees. 

The courses offered by these institutes start after class 12 for several LLB courses, thus it leads to absolutely no question about you having time to pursue a job. The reason is that it is impossible to pursue a job while pursuing a course as vivid as the one mentioned above. The degree you will acquire is not a part-time degree that is easily feasible at several second-tier universities.

The classes usually extend from 9 A.M. to about 12.30 P.M., while the afternoon classes commonly stretch from 2 P.M. to 4 P.M.

However, in case you are pursuing a distance learning program, which does not include L.L.B, then you can undeniably continue your job.