With big sister Lila...
Daisy - Eh, falls way short. I'd feel robbed if I was a Daisy with a big sister Lila.
India - I have no love for this name on children who aren't of Indian ancestry. If your daughter is, then I think it pairs well with Lila.
Clara - Same as Daisy, falls short. I'd feel robbed.
Poppy - Same as Daisy, and Clara.
Esme - Has such a different feel from Lila, it can work, but it feels a bit forced.
If I had a daughter named Lila, and was pregnant with another my ideas would be:
Though my tastes my be very off from yours.