In the meantime, melt the 1/4 cup of butter with the 1/4 cup of oil in a small saucepan over medium heat. Add the flour and stir until smooth, about 3 minutes. Blend in the stock, stirring until thickened, about 1 minute.
Reduce heat to low. Add the garlic, parsley, lemon juice, salt and pepper. Cook 5 minutes, stirring constantly.
Blend in the artichokes and the 2 tbsp of parmesan cheese.
Cover and simmer over low heat for about 8 minutes.
Melt the remaining butter in a large skillet over medium heat. Stir in the remaining oil, cheese, and salt. Add linguine and toss lightly.
Arrange pasta on a platter and pour sauce over all. (I usually just toss it all together.).
Serve immediately. (It still tastes good as leftovers too.).