If Lilly's numbers are rising, it's generally fine to shoot. Remember, Lantus onset isn't immediate. The insulin will start to work in approx. 2 - 3 hours and you will have food on board.
The big issue here is you have no spot checks. You don't actually know when Lilly's onset or nadir is. If you are at work during the week, then get some tests, the bare minimum is a test before you go to bed, at night. Get a "sleep" test (i.e., set an alarm, get up, test, and go back to bed). Given the sparsity of data, I don't know how to best advise you. If you shoot, you MUST test.