Preheat oven to 425°. Place mahi-mahi on a rimmed baking sheet and rub all over with 1 Tbsp. oil; season on both sides with salt and pepper. Brush or rub fish on both sides with 1 Tbsp. plus 1 tsp. mustard. Using a Microplane, finely grate zest of lemon over fish. Set lemon aside.
Bake mahi-mahi until opaque throughout and flesh flakes easily with a fork, 8–10 minutes.
Meanwhile, heat 1 Tbsp. oil in a large skillet, preferably cast iron, over high. Cook asparagus, turning occasionally, until blistered in spots, about 4 minutes total; season with salt.
Remove mahi-mahi from oven. Cut reserved lemon in half and squeeze juice from 1 half over fish. Squeeze juice from remaining half into a medium bowl (catching any seeds with your other hand). Add honey, remaining 1 tsp. mustard, and remaining ¼ cup oil and whisk until smooth; season dressing with salt and pepper.
Add avocado and arugula to dressing and toss gently to coat. Taste salad and season with more salt and pepper.
Divide fish and asparagus among plates and scatter salad on top.