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Since at least one name in Lillian's name is honoring, I'd have at least one name for the other child be honoring too.

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I would choose between
Eve Rachel - though I think Eva Rachel would flow better
Grace Luila - cool sound to this one, I like it a lot. Personally this would be my choice.
Hope Rachel
Natalie Ruth

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If you really hate Liv, I would hesitate on Olivia, because someone will inevitably call her Liv. I think Vivian is too similar to Lillian. Tongue twister there.

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Since Lillian might have 2 middle names, here's some ideas
Brooke Olivia Ruth
Hope Rachel Eve
Natalie Grace Luila