Likelihood of that is low, based on the sheer fact how Kobra was trying to have Vivi get married, but no doubt it's a certain possibility. However, that's only to my point. Folks are acting as if the King of Alabasta existing isn't the other possibility and jumping straight to conclusions about Imu-JB-Lilly.
-> The 20 Kingdoms defeated the Ancient Kingdom, she was still the queen at the time
-> The 20 Kingdoms formed the world government, she was still the queen at the time
-> She then for some reason left her country and went missing.
So she took part in the 20 kingdoms whooping Joyboy and his kingdom's ass, and then helped even form the organization that would become the World Government. But after she refused to live on Mariejois, she for some reason leaves her country and is never heard of from again.
The likelihood of some love triangle is very low to me. More than likely she was a friend of some sort of Joyboy's, similar to the princess of FMI. But considering how the Gorosei still resent Alabasta to this day, I highly doubt it's related to some love triangle, but more of Lilly just being that big of an entity who was a solid Queen that made decisions that didn't coincide with the rest.
People are literally assuming a love triangle cause this mf Imu came and said her name, lol?