I can't find any specific type of arthropathy with the documentation of Facet Arthropathy, lumbosacral, chronic so coding M12.88 other specific arthropathies doesn't have any supporting documentation,
spondylopathies is a general term for disorders of the vertebrae
spondylosis is a painful condition of the spine resulting from the degeneration of the intervertebral disks.
coding spondylosis would be incorrect as the definition states that it is a "degenerative" disease of the intervertebral "disks" the documentation states Facet Arthropathy.
also arthropathy may be used regardless of whether there is inflammation or not. look for any supporting documentation for an inflammation like increase Prostaglandin, even if facet arthropathy is usually associated with rheumatoid arthritis, osteoarthritis, or traumatic joint disease, coders can't just assume that this is an inflammatory disease.
M12.9 should be the code for this, ask the physician for specificity of the patient condition whether it's neuropathic (Charcot), gouty, enteropathic, crystal induced, infectious, inflammatory (arthritis) etc..