From the experts:
Lula is one of the livelier nickname-names with the fashionable double-L sound: It joins Lulu, Lila, Lily, and Lou among the trendiest names today. Lula might be short for Talula and sisters or for Lucy or Louise, or may stand on its own two adorable feet. Lula was actually a Top 50 name in the late 1880's and continued in the Top 100 for a couple of decades more.
Bryan Adams named his second daughter Lula Rosylea, sister of Mirabella Bunny, and master character namer J. K. Rowling has a Lula in her novel The Cuckoo's Calling.