It looks to me like Mimi is bouncing. If you go back to 5/14, she dropped dramatically into the greens, you skipped a shot the next AMPS, and numbers eventually zoomed up. She dropped back into the blues by the next AM cycle and then bounced again. You're seeing the results of the bounce.
Bounces are enormously frustrating -- to us! They are the result of numbers dropping low, numbers dropping fast, numbers dropping into a range your cat isn't used to spending time in, or a combination of the above. As a result of the drop in numbers, your cat's liver and pancreas release a stored form of glucose along with counterregulatory hormones that cause numbers to spike upward. It's a protective mechanism. As Mimi gets more accustomed to spending time in lower ranges, the bounces will occur less often. The good news is that while a bounce can last around 3 days, she's clearing them fairly quickly. As an example, Mimi dropped from a high of 642 at AM +6 on 5/17 to 272 at PMPS. There is a possibility she may zoom back up given the almost 400 point drop or the numbers may continue to drop.
One observation -- Lantus dosing is based on the nadir (the lowest number in the cycle). You don't base your dose on pre-shot numbers. Because Lantus is a depot-type of insulin, you don't want to change doses too quickly since it doesn't allow the depot to catch up with a dose change. If you opt to follow TR, you hold a dose for 3 days/6 cycles. You increased to 0.5u a bit too soon and it looks like you were basing the dose on the highs that you saw. In the grander scheme of things, the 0.25u dose was bringing Mimi's numbers into the greens. It's hard to evaluate how effective that dose has been given some of the skipped shots. Every time you skip a shot, you are emptying the depot a bit which means you're not going to have a good sense of how well the dose is working. One other thought -- as I noted above, you saw a BIG drop during the AM cycle to your PMPS. Shooting a dropping number can make for an "exciting" cycle especially since you raised the dose. There can be considerable momentum behind a dropping number. If you shoot and raise the dose at the same time, you could be up for a while feeding your kitty lots of high carb food in an effort to keep numbers from dropping too low.
So now that I've thrown all of this information at you, sometimes it doesn't apply. Ketones are the one thing that throws all of this knowledge out the window. I'd encourage you to keep testing for ketones and put the information on Mimi's spreadsheet. I'm always leery when it comes to telling someone who has a cat that's recently recovered from DKA to skip a shot. Ketones are just too scary to risk having happen again. Some cats that have been in DKA are quite prone to developing ketones again.