Put a skillet on at medium high. Whisk the olive oil and the lemon juice together in a bowl. Add the oiled lemon juice mixture to the skillet. Whisk in the dill weed, lemon pepper and basil. Whisk it a few more times as it heats up.
Carefully add the filets to the skillet. Spoon the liquid on the filets as they cook. They are going to cook pretty quick so just about a minute to a minute and a half each side. Maybe a little more depending on how thick your filets are. If you using thicker filets like tuna or cod cook more like three to four minutes a side. Fish is done when you lightly poke it with a fork and it wants to flake apart.
When you put the filets on the plates spoon some the liquid from the pan on them.
Enjoy your Friday Night Fish Dinner. For our wine tonight we had Gammy's favorite white, of course, Santa Margarita's Pinot Grigio.