Place a fine mesh strainer in a slightly larger mixing bowl and set it aside.
Peel and cut the cactus pears into quarters (heres how). Then add them to a blender and pulse until you have a smooth purée.
Pour the cactus pear purée into the strainer and, use the back of a large mixing spoon to help you drain all of the liquid into the bowl. (All of the tiny seeds will be held back in the strainer.) Get as much of the juice as possible -- you will need approximately ⅔ cup.
Add the lemon juice, vinegar and seasonings to the juice and mix. Then gradually whisk in the oil.