I always assumed they weren't Lapine, as they don't really follow the general naming scheme of other rabbits. I could see Lucy naming the rabbits Clover, Haystack, or Laurel, Boxwood being the only one that is a bit of a stretch. They're all nice kid names!
BUT if I had to say she renamed them...I'd say:
Clover: Snuggles
Laurel: Cuddles
Haystack: Rubbles
Boxwood: Grubbles