Both pretty - I prefer Lyla, I think.
Lots of similar names you could consider. You probably thought of all these but:
Ayla, Aria, Bella, Clara, Dana, Ella, Elsa, Freya, Isla, Iona, Jayla, Kayla, Kyla, Kyra, Kira, Lyra, Lena, Lila, Lola, Luna, Leah, Laya, Livia, Leona, Lara, Mila, Mala, Mara, Mira, Mika, Maya, Mia, Myla, Nyla, Nola, Nova, Nyah, Nia, Orla, Rosa, Sara, Skylar, Summer, Tia, Tara, Una, Veda, Willa, Zara, Zia, Zillah, Zelda.