The Andúril UI was developed by
reddit user and BLF member
ToyKeeper, who also developed the earlier Narsil UI. The UI names are borrowed from J.R.R. Tolkien's epic trilogy,
The Lord of the Rings: Narsil was a longsword wielded by King Elendil during the War of the Last Alliance and used by his son, Isildur, to cut the One Ring from Sauron's hand during the final battle of that war, being shattered in the process. It consequently was known as the Sword that was Broken. Narsil was much later reforged into Andúril, and would become the sword of Aragorn II Elessar Telcontar, aka the ranger Strider.
As far as what the inspiration for these flashlight interfaces are... I'm not sure the question makes a lot of sense, unless it be that ToyKeeper wanted a decent, usable, complex flashlight interface, and this desire inspired her to develop Narsil, which like the sword of the same name, was further developed into Andúril. I think it's probably unlikely she owned or knew of the LiteFlux interface, and I don't see much similarity between Andúril and the LF3XT interface. When you only have one button, superficially all flashlight interfaces may seem to be similar. The LF3XT is dominated by a double press, which is very rarely used in Andúril.