Pre-heat the grill on high head and place trimmed asparagus spears in a resealable plastic bag. Add olive oil, ½ teaspoon of the salt and black pepper to the bag. Seal and shake well to coat.
Grill asparagus on high heat until charred on both sides, about 5-6 minutes flipping once halfway through.
While the asparagus is grilled, begin making the lemon tahini sauce. To start, whisk together the lemon juice, tahini, garlic and remaining ½ teaspoon salt in a small bowl. Working 1 tablespoon at a time, whisk in warm water until sauce becomes smooth and you've reached designed consistency.
Arrange grilled asparagus on a platter and drizzle with the lemon tahini sauce before topping with toasted almond slices to serve.