Is the Polymyalgia Rheumatica suffered by my client caused by a chronic viral infection? Is that the reason I was shown by her deep subconscious three parallel lives of what appeared to be fatal viral disease episodes?

Both of these things are accurate and true. It is a perfectly logical extension of what you know already and were seeing intuitively, and in addition makes sense that a current medical condition causing pain and discomfort would trigger prior karmic events to be on the radar of the deep subconscious and vice versa, that the karmic history would predispose an individual to have a chronic condition in the current life that mirrors extreme traumatic events in other lifetimes, because very few things in the physical realm receive healing while they unfold, as humans lack the knowledge and training to do so effectively. So the parallel lifetimes suffering severe impairment and death from infectious disease nicely parallels the current suffering and is a causal element. Doing the healing work will break this cycle and remove the karmic need to re-experience chronic illness of this kind in the future.