Hi Ann & Liz,
Taking Lila's age into consideration it's a good idea to get a very full blood work-up including kidney and liver markers - if only to use as a baseline for the future. I'd ask for B12/folate, Spec fPL (pancreatitis and diabetes are often comorbid but, again, it's a valuable baseline to have and sometimes it can be an occult problem) and also thyroid. Other members may suggest additional things to consider.
Re the constipation, poorly regulated diabetes can affect stomach emptying and gut motility (diabetic gastroparesis). B12 methylcobalamin supplementation helps with neuropathy; I'm not sure whether it might also be helpful with GI motility issues but it might be worth picking your vets' brains about this.
Looking at Lila's spreadsheet (with a now-working link!) I think it would be an idea to discuss a Caninsulin dose increase to 1.5IU to be held for 5-7 days. This is on the assumption that your vet may need to order in Prozinc. If the vet can switch Lila to Prozinc sooner then, based on her clinical signs in response to the Caninsulin, if she were my cat I'd be inclined to push for the switch to the new insulin (at a low starting dose with a view to following the FDMB Prozinc dose adjustment method).
When speaking to your vets about the Caninsulin side of things be sure to flag - in mile-high letters - that MASSIVE drop from 24.1 AMPS down to 5.4mmol/L at AM+6 on 02.10.16 and tell them about how poleaxed Lila was as a consequence. Given the action profile of Caninsulin she may have been even lower than 5.4mmol/L between +3 and +6 on that cycle. It's way too fast and too steep a drop - and the dose is unsafe.
As well as getting the vet to check ketones (bring a urine sample with you as they may not have a blood ketone meter) pick up some urine test strips ASAP and test daily at home as a part of Lila's regular monitoring programme. Ketones can appear suddenly and build up very quickly so intermittent testing isn't sufficient.
Mogs
.