Heat oven to 400°. Lay pieces of bacon flat on a nonstick pan and bake, periodically draining off the fat. When bacon is crispy, place on a paper towel and cool, then break into bite-size pieces.
Boil potatoes and strain. Let sit until dry. Take basil leaves and thinly slice them with a sharp knife, cutting them without bruising them. Juice the lemons and add the basil. Then add both to the mayonnaise. Use a fork to whisk in other spices until blended. Pour the mixture over the dry potatoes, add the bacon and mix. Season to taste.