Clean the clams by soaking them in fresh water for 20 minutes. Proceed with the recipe while the clams are soaking.
Cook linguine according to package directions. Drain and return to empty pot. Toss with 2 tablespoons of olive oil. Set aside.
In a large skillet over low heat, heat the butter and remaining olive oil until the butter has melted. Add the garlic and cook until fragrant, 30 seconds. Do not let the garlic brown.
Remove the fresh clams from the water and add to the butter. Stir to coat. Increase the heat to medium, cover and let sit until the clams open, about 5 to 8 minutes.
Reserve the clam juices in the skillet by using a slotted spoon to remove the clams to a clean bowl. Discard any clams that don't open.
To the skillet, add the lemon juice, wine, tomatoes, and parsley. Bring to a simmer and cook, stirring occasionally, until reduced and slightly thickened, about 5 minutes. Stir in the canned clams and cook until heated through.