Bacteria

No, Lyme disease is caused by the organism Borrelia burgdorferi which is a spirochaete and must be carried by an arthropod (insect host)

A spirochete (also spelt as Spirochaete) is Prokaryotic.

Spirochaetes is a phylum of distinctive Gram-negative bacteria, which have long, helically coiled cells.[1] Spirochetes are chemoheterotrophic in nature, with lengths between 5 and 250 µm and diameters around 0.1-0.6 µm.[citation needed] Spirochaetes are distinguished from other bacterial phyla by the location of their flagella, sometimes called axial filaments, which run lengthwise between the cell membrane and outer membrane. These cause a twisting motion which allows the spirochaete to move about. When reproducing, a spirochaete will undergo asexual transverse binary fission