Headcanon: Luna often got called “Auntie Lulu” by Lily when she was a little girl, because when she was 1-2, she couldn’t get “Luna” out properly. so Luna just got her to say “Lulu”.
"Alec, calm down." Clara chuckles as the the baby boy waddles around the living room. "Par-ee! Par-ee!" He chants happily. "We'll go to Auntie Lulu's house for your party in a bit. First you need to get dressed."