Never tried the Lair but I like the Cave. I can confirm that it is a swine to pitch, particularly at dusk, when the black guys are difficult to see let alone work with. Altering the position of one peg seems to create a need to alter two other pegs. Nevertheless, perseverance brings a satisfactory result.
The beaks are particlularly useful in windy conditions. I pitch the back low, often, but not always, with the beak closing the end of the tarp. The front is as high as possible, with the beak horizontal, for easy entrance and exit. If I always closed the back, then you could say that a Lair would have been a better purchase, but I don't because it is not always windy.
By the way, I rarely rig the side lifters so only need two trekking poles and no supplementary twigs. (My tarp camping is usually well above the tree line.)