Cut cucumbers lengthwise into 1/4-inch-thick slices.
Combine cucumber slices, pickling lime, and water to cover in a nonaluminum stockpot; stir well. Cover and let stand at room temperature 12 hours.
Drain cucumbers; rinse with cold water, and return to stockpot. Add fresh cold water to cover, and let stand 1 hour. Repeat procedure 2 times. Drain cucumbers, and return to stockpot.
Combine vinegar and next 3 ingredients in a saucepan; bring to a boil over medium heat, stirring until sugar dissolves. Pour vinegar mixture over cucumbers in stockpot; cover and let stand 6 hours or overnight.
Bring cucumbers and vinegar mixture to a boil over medium heat; cover, reduce heat, and simmer, stirring gently, 35 minutes.
Pack cucumbers into hot, sterilized jars. Pour vinegar mixture over cucumbers, filling to 1/2 inch from top. Remove air bubbles; wipe jar rims. Cover at once with metal lids, and screw on bands.
Process in boiling-water bath 5 minutes. Refrigerate pickles after opening.