As you said
@mirror, the data is stacking up to do 2-3 u of Lantus twice a day. Well, the good news is we were looking for the low point and now we've found it, so we can build up again. Much safer to have high BG and increase insulin than the other way round.
Try 2-3u Lantus 2/daily and see if we can get to the point where we are also giving bolus doses.
Any idea of her carb ratio? With a correction ratio of 1u:>12 mmol/L I expect her carb ratio will be similarly very high, because both things reflect insulin sensitivity and her insulin sensitivity is insanely high at the moment, for whatever reason. So be very cautious on the bolus doses if and when we get to them. Like start at 1u:30gCH or 1u:25gCH, something like that, and work up slowly from there.