Does the name begin loon or lyoon?
heard as lyoonularia
spelled lunularia
Both are heard, and lyoonularia is written lunularia either way.
What the ear did
This is the long u of English, the one that carries a hidden y sound. Whether you hear it depends on where you learned to speak: tune, duke, lunar and lucid keep the y glide in southern British English and lose it in most of North America, so the same genus is loo-nu-LAIR-ee-a in one place and lyoo-nu-LAIR-ee-a in another. The spelling does not take sides. A single u covers both, exactly as it does in luna, lunar and lunate, and there is no letter anywhere in Latin for the glide. The moon is the point of the name. Lunularia carries crescent-shaped cups on the surface of its thallus, each one holding a stack of green gemmae that rain splashes out, and lunula is the Latin for a little moon.
L-U-N-U-L-A-R-I-A
The full entry for lunularia covers the name itself.