In mixing bowl, toss lamb with onions. Add a large handful of herb mixture and oil, and toss to coat.
Place lamb and onions as snugly as possible on bottom of very large enamel cast-iron pot. Set pot over high heat and cook until steam begins to rise from bottom, about 3 minutes. Reduce heat to medium-low, cover with tight-fitting lid and cook until lamb is opaque and has thrown off a lot of juice, about 12 minutes. Turn lamb, cover and cook for 3 to 4 minutes longer. Add chopped tomatoes, another handful of herbs, 1 cup tomato juice and 1 tablespoon vinegar, and bring to a vigorous simmer. Cover and transfer pot to oven. Cook until lamb is tender, 1 1/2 to 1 3/4 hours, checking periodically and adding a little water if it looks dry.
While meat cooks, char eggplants either directly on 3 burners set over medium-high heat on gas range or by putting under a broiler. Cook, turning and moving eggplants until surface is lightly browned and begins to char in spots but the flesh is still firm, 2 to 3 minutes total. Watch out for drips and flame sparks. Using tongs, transfer eggplants to cutting board. When cool enough to handle, cut each eggplant crosswise into 4 sections. With small knife, make a slit in each section and stuff some of the herb mixture into each slit. In 2 separate bowls, season potatoes and quartered tomatoes with salt and a little of the herb mixture.
Remove lamb from oven and stir in potatoes, using tongs and a large spoon to push them gently under the meat. Add remaining tomato juice and vinegar, another handful of the herb mixture and enough boiling water, if needed, to generously cover the potatoes and meat. Scatter eggplant sections on top, nestling them in liquid. Cover and bake for 30 minutes longer. Add quartered tomatoes, scattering them on top without stirring, and sprinkle with remaining herb mixture. Cover and bake for another 20 minutes.
Raise oven temperature to 400 degrees. Uncover pot and bake until juices are thickened, about 15 minutes. Remove stew from oven and let cool for 5 to 10 minutes. Serve straight from the pot, sprinkled with additional herbs.
Nutrition information per each of 8 servings: