It seems logical that tau and synuclein occur simultaneously (but not in the same brain areas) if you admit that they have the same risk factor. This factor is likely APP dysfunction since you have an amazing load of amyloid plaques in sporadic Lewy body dementia, totally similar to those of AD in quality and quantity.
References: Deramecourt V et al. Biochemical staging of synucleinopathy and amyloid deposition in dementia with Lewy bodies. J Neuropathol Exp Neurol 2006;65:278-288. Abstract.