In a large nonstick skillet, heat 1 tablespoon of the oil until shimmering. Add the greens and cook over moderately high heat, stirring, until tender, 1 1/2 minutes; season with salt. Transfer the greens to a bowl and keep warm.
In a small bowl, mash the avocado. Stir in the lemon juice and season with salt.
Add the remaining 1 tablespoon of oil to the skillet. Crack the eggs into the pan and season with salt. Cook over moderate heat until the whites are crisp, about 1 minute. Flip the eggs and cook until the whites are firm and the yolks are runny, 2 minutes longer.
Spread the avocado on 4 of the toast slices. Top with the greens and fried eggs and sprinkle with the hot sauce. Close the sandwiches, cut in half and serve right away.