I don't remember any quests (aside from the NCR diplomacy ones) in which you could actually make quest progress by going directly to Lynette. Try retracing your steps and see if you missed an important dialog option/item to hand over to Sark or Lynette. My memory is fuzzy, but otherwise I'm not sure what options you have.
Other than that, Lynette is a 'tough' one... there are many fast, easy and fun ways to anger her if you are not extra careful and diplomatic, so is it possible that she just doesn't like you very much?
Without a doubt. I don't believe
any of the potential slavery/xenophobic/NCR debate conversations you can engage in with her end well. At least, for me, being thrown out has always been inevitable. Of course, nothing is more fun than pickpocketing a ticking stick of dynamite on her person and fleeing to the other map section of the town (otherwise NPCs will turn hostile even if you are out of their line of sight).