Priya,
Anand told Lavanya about Thamizh trying to talk to Thulasi about his engagement and left out Thamizh's attempts to let Charu know (purposely, of course!) . So, Lavanya decided to do what is best for her brother and what Thamizh did not have the courage to do . I agree with you that she's gullible, not selfish. More importantly , Lavanya talked about Thulasi day in day out, so she's more responsible for the mess Thamizh is in right now and it makes sense for her to approach Thulasi and put everything right for her brother.