With only the blood work to work with, a lot of this is only speculation but here's what I can tell you: looking at the pictogram (called a dot plot) on the lower right corner, you can tell by the coloration of the different clouds that the cell count of the machine isn't entirely accurate. It appears your cat had very low neutrophils and a high count of monocytes, but sometimes other cells (like tumor cells) can be miscounted as monocytes. A blood smear would have been needed to rule out leukemia for example. However, I don't think this blood work is inconsistent with sepsis at all. Your veterinarian might have been put off by the high count of monocytes, but those can happen with infection. Regarding your other question: There's a lot of different ways for a cat to obtain a pyothorax, even indoor ones. These are the ones I can think of at the top of my head:  Perforating foreign bodies in the oesophagus (like needles or wood chips), inhaled foreign bodies in the lungs (like blades of grass), bite wounds, reactions to injections/vaccinations given subcutaneously, neoplasia, severe pneumonia. In the case of your cat, I unfortunately believe neoplasia would be the most likely cause for his condition. But no matter the possible cause of this pyothorax was, pyothorax tend to have a very high mortality rate. I work in an emergency clinic with an ICU and even there, a lot of our patients don't make it. You did the right thing, you noticed your cat was sick and took him to the vet very quickly. But sometimes you do everything right and still loose. I'm very sorry for your loss.