Remove outer green skin and pink flesh of watermelon rind. Cut greenish-white portion of rind into 1-inch cubes or other shapes, if desired.
Place rind in a large glass, ceramic, or stainless steel container. Combine lime and 1 quart cold water; pour over rind. Cover and let stand in a cool place 3 hours. Drain and rinse in 3 baths of cold water.
Place rind in a 10-quart stainless steel stockpot; cover with cold water. Bring to a boil, and boil slowly, stirring occasionally, 1 hour or until rind is translucent. Drain well.
Combine rind, 2 cups water, and 1 cup vinegar in a glass container; mix well. Cover and let stand in a cool place overnight. Drain; cover and set aside.
Combine cinnamon, cloves, and allspice; tie loosely in a cheesecloth bag. Combine spice bag, remaining 1 cup water, 3 cups vinegar, and sugar in stockpot. Bring to a boil; remove from heat. Cover and let stand 1 hour. Add rind to syrup. Bring to a boil; reduce heat, and cook over low heat, stirring occasionally, 2 hours or until rind is translucent. Remove spice bag; discard.
Pack rind into hot sterilized jars; pour syrup over pickles, leaving 1/2-inch head space. Remove air bubbles. Cover with metal lids, and screw bands tight. Process watermelon rind in boiling-water bath 15 minutes.