Institutions which are approved under the criterion laid down by the apex organisation UGC, are allowed to conduct the different courses and award degrees to the students. UGC, time to time, checks the functioning of these institutions physically as well as online audit by questionnaire and document verification and if finds anything adverse, blacklists such institutions and posts it in its site www.ugc.co.in and anyone can check the credentials there if there is any doubt in that respect.
LLM course through distance education from the Acharya Nagarjuna University, Andhra Pradesh is an approved program by UGC and there is no problem on that account.
Now, doing a masters is not sufficient for a lecturers job and one has to qualify NET test for it. NET is a national level test and one has to de adequate preparation to qualify for that. After qualifying NET, one can apply against the post of lecturer in any place in India.
Some private institution, coaching centres and donation colleges do not insist for NET and appoint the lecturers on ad hoc basis but then the associated risk of getting shunted out anytime plus relatively lesser salary is a matter of concern.
Knowledge is power.