I think Poppy has been in vogue for the last ten years or so, and I always associate the name with a middle class, precocious verging on irritating/naughty little girl who knows she can twist her parents around her little finger to get what she wants.
Lucy is a classic name that is never really in or out of fashion and I don't really have any strong feelings about the type of girl that would be called Lucy.
You could also consider Lucia with the option to use Lucy or Lucie as a nickname. I always think Lucia is very beautiful and elegant, especially for an adult woman.