Wash and scrub the pickling cucumbers, and then remove the stems and cut off the blossom ends.
Slice cucumbers into 1/4 inch (or thinner) slices.
Mix the pickling lime in water to create a soaking solution.
Place the cucumber slices into a non-reactive container (glass, ceramic, stainless steel, plastic, etc.). Avoid aluminum or copper containers, as the lime will react with the container, ruining the container and the pickles.
Pour the pickling lime solution over the cucumber slices, and weigh them down with a plate to ensure they're completely submerged.
Soak the cucumbers for about 12 hours, or overnight. Stir occasionally, if possible, to keep the lime evenly distributed in the water.
After the soak, pour off the soaking water and discard. Rinse the cucumbers 3 times in clean water, making sure that you remove all the lime from their surfaces and the container.
Soak the cucumber slices in clean ice water for 3 hours to chill them and remove any last bits of extra pickling lime.
Drain and discard the soaking water.
Prepare a pickling brine by mixing the vinegar, sugar, canning salt, and pickling spice. Unlike other pickling recipes, the brine should be room temperature at this point.
Pour the room-temperature brine over the prepared cucumber slices and let them stand for about 6 hours, or overnight. Cover to keep out pests, and refrigerate if possible.
After the brine soak, drain the brine into a stock pot (straining out the cucumber slices for now) and bring it to a boil. Turn the heat down to a simmer and simmer the brine (without the cucumbers) for 35 minutes.
While the brine is simmering, prepare a water bath canner by pre-heating it for raw pack (about 140 degrees F) and also prepare jars, lids and rings.
Pack the cucumber slices into prepared jars. They can be packed quite tightly as they'll shrink during canning. Be sure to leave 1/2 inch headspace.
Once the brine has simmered for 35 minutes, bring it back to a boil and pour the boiling brine over the cucumber slices in the jars, maintaining 1/2 inch headspace.
Debubble the jars, adjust headspace, and seal with 2-part canning lids to finger tight. Load the jars into the pre-heated canner.
Bring the canner up to a full rolling boil, then process pints for 10 minutes or quarts for 15 minutes, adjusting for altitude (see notes).
Turn off the heat, take the lid off the canner, and let the jars sit in the water for 5 minutes before lifting them out.
Let the jars cool on a towel on the counter for 12 to 24 hours, then check the seals. Refrigerate any jar that didn't seal, and store sealed jars on the pantry shelf.
Wait at least 2 to 3 days before tasting so the cucumbers can pickle. They'll be much better after 2 weeks.