Is it necessary to wear hijab while watching a majalis or lecture within our house? I understand when we go to Imam baragah we must observe hijab due to non mahram being present. But if I am home within my family is there any tradition that recommends wearing hijab while listening a lecture or not?

No it is not necessary to wear Hijab while watching a lecture or Majles. Some women do so just to show their respect for the Ahlulbayt (a), but it is not mandatory to do so.