Combine the lemon juice with 1/2 cup olive oil in a sealable plastic bag; seal and shake. Add the tuna steaks and store in refrigerator to marinate while the grill preheats.
Preheat an outdoor grill for high heat, and lightly oil the grate.
Whisk the brown mustard, mustard powder, sugar, vinegar, and 1/3 cup olive oil together in a bowl; stir in the dill.
Remove the tuna from the marinade and discard the marinade; cook the steaks on the preheated grill until the fish flakes easily with a fork, about 6 minutes per side. Drizzle the steaks with the mustard and dill sauce to serve.