First off, let's try to forget our preconceived notions about training as we approach this question. I'm not asserting any idea, just asking a genuine question.
Second, let's define terms since different people mean different things when talking about these things. LT1 is the onset of blood lactate accumulation (OBLA) or the point where your mitochondria can no longer process lactate as a fuel source as quickly as you're producing it & so it starts accumulating in your blood.
LT2 is generally said to be the point along your lactate curve where lactate begins to increase at an even faster rate. Breathing becomes considerably more labored.
And herein lies my confusion. Notice the definition for LT1 is based in physiology. The definition for LT2 is based... on subjective feel? A change in the relationship of the curve? I know people will say that the increase in blood lactate concentration (BLa) is faster after LT2, but the only real change in relationship occurs at LT1 - it goes from very stable BLa to being the start of the exponential increase. Nothing changes mathematically at LT2 - that's just what an exponential curve looks like. It gets steeper. (I'll admit, I'm no math expert so correct me if I'm wrong here. Even if I am though, I think the point still stands).
Sure, there is a difference subjectively at LT1 vs LT2. LT2 will feel much more laborious. Your breathing intensifies, and you'll reach failure relatively quickly. But I'd argue you'll reach that point of labored breathing & fatigue at any point above LT1 provided duration is long enough. It might take 90-120min if you're just above your LT1, but you'll eventually be very fatigued. As an example, if you were to truly race a half 'thon and pace it well, right at your limit, you will be hurting bad at the end.
So my question what is happening physiologically at the LT2 intensity that's different at the LT1 intensity? One could argue that you're not really doing anything other than creating more muscular fatigue than necessary. If you can get the same adaptations you want from LT training at the LT1 intensity - that being increased mitochondrial efficiency/density to better utilize the lactate thats being produced as a fuel source (i.e. lactate clearance) - why would you push yourself any further?
I understand elites do LT2 work quite often. Ingebrgitsen double threshold, etc, etc. The reality is we don't really know what intensity they are training at when they do LT work. Also, I'm looking for an answer based in physiology not a case study. What specifically changes between LT1 and LT2? Do we know? Are there any theories in the literature?