Pat lamb dry; season with salt and pepper. Let sit at room temperature 1 hour.
Meanwhile, purée sorrel, mint, parsley, lemon zest, red pepper flakes, about 1 garlic clove, and ⅓ cup oil in a blender, scraping down sides as needed, until mixture is smooth. Season salsa verde with salt and pepper; set aside.
Prepare grill for high heat (or heat a grill pan over high). Grill chops, turning every 2 minutes or so, until well browned and beginning to char and a thermometer inserted into the thickest part registers 125°, 8–10 minutes. Let lamb rest at least 10 minutes.
While lamb is resting, heat remaining 2 Tbsp. oil in a large skillet over medium-high. Cook mushrooms, tossing occasionally, until well browned, about 4 minutes. Transfer to a large plate.
Reduce heat to medium and add shallot and remaining garlic to skillet. Cook, stirring occasionally, until shallot is softened and starting to brown, about 2 minutes. Add greens; season with salt and pepper. Cook, stirring occasionally, until wilted and bright green, about 2 minutes. Return mushrooms to skillet and toss to combine. Stir in vinegar; season with salt and pepper.
Stir lemon juice into salsa verde; taste and adjust seasoning with salt and pepper. Serve lamb chops over mustard greens with salsa verde.
Do Ahead: Salsa verde (without lemon juice) can be made 1 day ahead. Cover and chill. Add lemon juice before serving.