Wash the whole cucumbers and remove any dirt. Cut off and discard the ends. Then slice the cukes into rounds 1/2" thick.
Mix the lime and several cups of water in a large ceramic, stainless steel, or enamel container. Stir until well-blended. I wear a mask - the lime has a way of getting in the air.
Add more water to the lime mixture and stir. Add the cut cucumbers. Add enough water to cover the cucumbers. Using a wooden, plastic, or stainless steel spoon, stir to mix the lime into the water and cover the cucumbers. I wear gloves, you really don't want the lime on your hands. Be careful -- the cucumbers will break easily. Soak 24 hours or overnight. Stir several times to blend the lime. Use your hands or the spoons to stir the lime mixture. You can also soak for 2 days if something comes up.
After soaking overnight, drain cucumbers and rinse in clear water. Let sit in the clear water and rinse every hour on the hour for a total of 4 times. In other words, you will drain and put fresh water in the bowl 4 times. Do a final drain.
Pour 1/2 gallon of the 5% white distilled vinegar into a large stainless steel or enamel cooking pot (I use a big soup pot).
Start heating the vinegar and stir in 5 pounds of sugar. Using a piece of double cheesecloth about 6" square, tie up 3 Tablespoons of pickling spice and put that in the sugar-vinegar mixture. Cook and stir until the sugar is melted.
Add the drained cucumbers and bring to a boil and then turn burner off. Let stand overnight.
The next day bring the pickles to a boil and boil for 1 hour.
Take the sliced cucumber pickles out of the pot and drain in a colander, reserving the pickle juice. Remove and discard the spice bag. Move the pickles to a large plastic bowl. Working in batches, chop pickle slices into relish-sized pieces. Return the relish to the pot with the hot vinegar mixture, keeping the mixture warm.
Put relish in the jars and fill with the pickle juice, filling jar to 1/2" from the top. See below for instructions.
To process in hot water bath, see below.