Remove twine from lamb and trim off all but a thin layer of fat. Pat dry, season generously with salt and pepper, and rub with 1 tbsp. oil. Unfold roast and season inside the same way. Chill 1 to 2 days.
Blanch mint 3 to 4 seconds in a pot of boiling water (this will help keep leaves bright). Drain immediately, rinse with cold water, and gently roll in paper towels to dry.
Put mint, almonds, 1/3 cup oil, the lemon zest and 2 tbsp. juice, the chile flakes, 1 tbsp. salt, and 1 1/2 tsp. pepper in a food processor and pulse into a coarse paste.
Take lamb out of refrigerator about 1 hour before cooking. Spread about a third of paste over inside of lamb, leaving a 1/2-in. border. To remaining paste, add 1 cup oil; season with salt, pepper, and more lemon juice. Set aside.
Roll up lamb and tie it at 1-in. intervals with kitchen twine.
Preheat oven to 450°. Heat a large cast-iron frying pan over medium-high heat. Swirl in 1 tbsp. oil and brown lamb all over, 5 to 8 minutes. Slide pan of lamb into oven and turn heat down to 250°.
Roast lamb, basting every half-hour with pan drippings and turning over halfway through, until it registers 135° at thickest part for medium-rare, 1 to 1 3/4 hours.
Let roast rest 20 minutes. Remove twine. Slice across the grain and serve with sauce.