Lucy (little cat):

• Luce (pronounced like "loose") / Luce-Luce
• Moo/Moomoo
• Miss/Missy/Missy Moo
• Wee One (as in little)
• Sweetheart/Sweetie-pie
• Miss Screechy

Sapphy (big cat):

• Sapphy is a nickname, her actual name is Sapphire. She's only ever called Sapphy though.
• Saph
• Madam/Madam Moo
• Big Girl
• Miss Bully
• Bossy Boots

Collective:

• Moos
• Pussycats
• Girls