With TR, you typically do not reduce the dose. To do so, means you're basing the dose reduction on the pre-shot number and with Lantus, regardless of the approach, dosing is based on the nadir. That said, if you think the pre-shot number is lower than where you're comfortable shooting, there are alternatives. However, you need to give yourself some time to get comfortable with shooting progressively lower numbers. If you look at Gabby's SS (or Marje's Gracie's SS), you'll see we would shoot any number above 50. It takes a bit of time and some nerves of steel to get comfortable with shooting low numbers.
You're also correct in that some cats are prone to experiencing lower numbers during the PM cycle. The problem with reducing the dose is that because you're using a depot-type of insulin, there's no guarantee that you'll see the effect of the dose reduction during the current cycle. The depot can have make up the difference. Also, every time you change a dose, with TR you need to wait 3 days/6 cycles before you can change the dose (dose reductions excepted). Any change in dose has an effect on the depot.
Gabby would also drop early in the cycle. I routinely tested a lot early in the cycle. I also front loaded her food. By that I mean that she was fed at pre-shot, +1, and +2. By spreading her meals into 3 installments, it helped to keep her numbers a bit "bumped up." You could try experimenting with a similar approach. If you see that numbers are dropping, you can add a bit more carbs to the mix, if necessary.