Preheat an outdoor grill for low heat and lightly oil the grate.
Combine oil and lemon juice in a baking dish. Add asparagus and roll until coated.
Grill asparagus on the preheated grill, turning at least once and brushing with remaining oil-lemon juice mixture, until crisp-tender, about 5 minutes. Remove from the grill and place back into the baking dish. Cut into bite-sized pieces.
Combine spinach, Parmesan, and almonds in a large bowl. Add asparagus along with any oil-lemon juice mixture from the dish. Toss to blend and serve immediately.