Add lemon juice, oil, garlic, rosemary, salt, cayenne, and lamb to a resealable plastic bag. Seal bag and place in refrigerator overnight, flipping bag occasionally.
Remove lamb from bag, disposing of marinade. Lay lamb on a rack in a roasting pan and bake at 325 degrees F for 80 to 90 minutes or until preferred doneness. Let cool to room temperature, wrap in plastic wrap and chill.
Combine artichokes and 2/3 cup of vinaigrette to a resealable plastic bag and let sit 10 minutes. Remove artichokes and dispose of vinaigrette.
Slice lamb into thin pieces and cut baguette in half. Take out inners from the bread leaving 3/4 inch shell. Drizzle about 2 tablespoons of the vinaigrette onto the bottom of each piece of bread and top with cucumbers, tomatoes, lamb, and artichokes. Drizzle the rest of the vinaigrette over top. Place the goat cheese on top and then the other halves of the bread. Wrap each sandwich with plastic wrap and chill. Slice to serve.