can a married woman Live in relationship with another man , she filed a case under section 498a

No she cannot have a live relationship with any other man because she is still married. The grounds to have a live in relationship are:

1) Both should be above 18 years of age.

2) If he or she is single/ divorced/ or the partner is dead. 

In this case, the women will not be considered to have live in relationship rather it is the case of adultery. 

Although adultery is decriminalised as per honourable Supreme Court, yet it can be used as a ground for divorce.

Here the husband can use this ground to file for divorce against her wife as there are no proof/evidence with the wife for the related case. If they get the divorce, then women can file for maintenance under section 125 crcp if conditions specified in the aforementioned section are fulfilled. 

Solemnization of second marriage without obtaining decree of divorce for first marriage is an offence u/s 494 IPC . That second marriage is nothing but an act of adultery on behalf of wife.

You may file divorce petition based on ground of adultery.

And last but not least, adulterous woman is not entitled for maintenance u/s 125 CrPC.

Regards
Mohit Chahal
Advocate
9968911099

You submit all relevant records to your lawyer and act accordingly