Just to add a couple more points:
1) Yes, wheelbase. Digging deeper, it's specifically the wheelbase relative to rear overhang ratio that's important. This ratio is the primary factor to which a trailer can influence the tow vehicles directional stability. A smaller ratio means the trailer has more leverage on the front axle. The Tundra obviously has the better ratio. But the takeaway here, is that with an advanced pivot point projecting hitch like a Propride, or Hensley, that the LC can be made just as stable.
I've heard the same thing. I had many trailer people tell me I should have a truck due to the much longer wheel base. In some cases that is offset but the distance from the rear axle to the tow point being longer creating more leverage for the trailer to effect "sway" or to "lever" up the front end a bit. The LC has a considerably shorter wheel base (great for off road but less so for towing) but at least the distance from the rear axle to the tow point is better.
BTW, I do use a Hensley which helps a ton. And the GVWR of our trailer is 6,000# so I keep the total loaded weight below that.
I also keep the tongue weight around 700 lbs. (Just measured it at 640 with full propane but no water.) The hitch weight max for the LC is 850 though I admit that even when using the weight distribution bars of my Hensley, the rear end sags a couple of inches. Which brings us to your next point
2) Suspension. The LC is designed with a plush suspension for ride, but also off-roadability. This is in contrast to the stiff suspension of the Tundrda, for load carrying. Compliance vs load bearing design goals. This is THE major factor to why the Tundra has more towing capacity. Takeaway again, is that by augmenting the stock LC suspension for additional load capacity, that it can be made to tow more again. Because we all know that the LC is surely heavy duty enough in architecture to bear greater loads.