Peel cucumbers, halve lengthwise, and scrape out seeds with a spoon. Cut halves into 1/4-inch half-circles and place into a glass or ceramic crock. Dissolve pickling lime in about 1 quart room temperature water, pour over cucumbers, then add additional water to cover cucumbers by 1/2 inch. Let stand at room temperature for 24 hours.

Drain cucumbers and rinse well with cold water. Place into a large stockpot and cover with cold water. Let stand at room temperature for 3 hours, then drain and rinse again.

Return cucumbers to the stockpot. Add 1 cup vinegar, food coloring, alum, and enough water to cover by 1/2 inch. Bring to a boil. Reduce heat to simmer and cook for 2 hours. Drain and let cool a bit before placing into the glass or ceramic crock.

Stir together sugar, remaining 2 cups vinegar, 2 cups water, red hot candies, and cinnamon sticks in a saucepan over medium heat until sugar and candies dissolve. Pour over warm cucumbers. Cover and let sit for 8 hours to overnight.

Pack pickles into hot, sterilized pint jars, filling to within 1/4 inch of the top. Run a clean knife or thin spatula around the insides of the jars to remove air bubbles. Wipe the rims with a moist paper towel to remove residue. Top with lids and screw the rings on tightly.

Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil and lower the jars 2 inches apart into boiling water using a holder. Pour in more boiling water to cover jars by at least 1 inch. Bring to a rolling boil, cover, and process for 15 to 20 minutes.