Dissolve lime in water in a large glass, ceramic, or stainless steel container. Add cucumber slices; cover and let stand in a cool place 24 hours. Drain and soak in cold water 4 hours, changing the water every hour. Drain and rinse well.
Tie pickling spices loosely in a cheesecloth bag. Combine spice bag, sugar, and vinegar in a stainless steel stockpot. Bring to a boil. Remove from heat; pour syrup over cucumbers. Cool. Cover and let stand in a cool place 24 hours or overnight. (Do not drain.)
Bring cucumber mixture to a boil. Reduce heat; simmer, uncovered, 25 minutes or until pickles are translucent, stirring frequently.
Pack pickles into hot sterilized jars; cover with syrup, leaving 1/2-inch head space. Remove air bubbles. Cover at once with metal lids, and screw bands tight. Process in boiling-water bath 10 minutes.