Lulu can be shut down by status. Customization isn't allowed for FFX characters in the DL is the general rule as far as I know. Lucia and possibly Yuri are protected from DC Death by Leonardo's bear. Lucia can status protect my other reviver or Songstress.
This doesn't matter for one reason. Yuna can kill the Songstress with Holy before she can act. Yes, Eiko can revive her, but I was under the impression that death sends you to the back of the line turn-wise (do some people believe otherwise?). Lulu's slow, but not don't-get-a-turn-until-next-decade slow. Outside of that, Yuna can OHKO Yuri or Lucia with Holy. The ID blocker is a good point if people allow them, but Lulu still has DC Flare, and that can off someone frail like Eiko or the Songstress.
Here's how I think it'll go, then. Yuna offs Songstress. Eiko (or Yuri, let's be generous for the sake of argument) revives, the other person does something, Lucia either protects Eiko or Songstress, doesn't matter, Nei sings, again, doesn't matter, I doubt she can prevent Lulu from going before Songstress at this point and unless I'm mistaken, and Yuna can get a turn before Songstress at this point anyways. Lulu DCs Flare, offs Eiko, and Yuna then smites Yuri with Holy. Game over. Songstress can only shut down one person and dies as soon as the other gets a turn. No muss, no fuss, no instant death. Feel free to correct me if I've made a mistake somewhere.
Of course, if Yuri *doesn't* have revival at this point, your team doesn't even make it this far due to Eiko getting offed by Hungry Friend and won't even make it past the BoF1 fight for the reasons cited above.