Put avocado leaves in bottom of a heavy medium pot with a tight-fitting lid. Sprinkle lamb shanks all over with 2 teaspoons salt and arrange in pot (they don't have to be in 1 layer). Roast, covered, until meat is very tender, about 3 hours.
Meanwhile, slit chiles lengthwise, then stem, seed, and devein. Tear chiles into roughly 1-inch pieces (you should have about 1 1/2 cups). Heat a comal or large heavy skillet (not nonstick) over medium heat until hot, then toast chiles, stirring constantly, until more pliable and slightly changed in color, 1 to 2 minutes. Transfer to a bowl. (Chiles will crisp as they cool.)
Cover tomatillos with water in a medium saucepan and simmer, uncovered, until tender, about 10 minutes. Drain well, then purée with chiles, garlic, cilantro, and 1 1/2 teaspoons salt in a blender (in batches if necessary) until chiles are ground to small flecks.
Transfer shanks to a cutting board to cool. Strain lamb juices remaining in pot into a glass measuring cup. Let fat rise to top and skim off. Coarsely shred meat, discarding bones.
Heat oil in a heavy medium pot over medium-high heat until it shimmers, then cook one fourth of tomatillo sauce (it will spatter), stirring, until slightly thickened, about 2 minutes. Add remaining sauce and lamb juices and simmer, stirring occasionally, 10 minutes. Add lamb. Thin sauce with water if necessary. Simmer, stirring occasionally, until heated through, about 4 minutes.
Cooks' notes: ·Lamb can be roasted and shredded 3 days ahead and chilled. Chill juices separately; discard solidified fat. ·Lamb in sauce can be made 2 days ahead and chilled (covered once cool).