There are still a few people who enjoy making their own pickles. Whether they are dill or sweet pickles, some prefer their own recipe. Do keep safety in mind when making pickles, especially when using lime.
If good quality ingredients are used in pickling and up-to-date methods are followed, lime and alum are not needed for crisp pickles. Soaking cucumbers in ice water for 4 to 5 hours prior to pickling is a safer method for making crisp pickles.
The calcium in lime does improve pickle firmness. If you choose to use lime, purchase FOOD-GRADE pickling lime from your grocer's shelves. Do not use agricultural or burnt lime. FOOD-GRADE lime may be used as a lime-water solution for soaking fresh cucumbers 12 to 24 hours before pickling them. However, excess lime absorbed by the cucumbers must be removed to make safe pickles. To remove excess lime, drain the lime-water solution, rinse and then resoak the cucumbers in fresh water for 1 hour. Repeat the rinsing and soaking steps two more times. Failure to remove lime adequately may increase the risk of botulism toxin.
Calcium hydroxide is needed for lime to work as a firming agent with cucumbers. Pickling lime is calcium hydroxide; so is hydrated lime. You may use hydrated lime, but it must be FOOD GRADE. Much hydrated lime is sold as pesticide, as ingredient for cement, or for other agricultural or industrial uses. If the label does not state that it is FOOD-GRADE, do not use it in making pickles. It may contain harmful substances if ingested. That would most likely include any of the lime sold in lumber companies or ag supply stores, but labels should be read or manufacturer contacted.
There are some high calcium hydrated limes sold for other uses, also, which will have closer to 72 to 74 percent calcium oxide rather than the 46 to 48 percent calcium oxide in "normal" hydrated lime. We do not know how this extra high calcium concentration would affect the firming for pickles, as only FOOD-GRADE lime is recommended for use. If you have FOOD-GRADE calcium hydroxide, I am not aware of any reason why the amount to use is different from one brand to another.
Do not use agricultural, burnt or quick lime. They are not calcium hydroxide. Burnt lime is burned calcium carbonate, which then becomes quick lime or calcium oxide. Quick lime is also called caustic or hot lime. When water is added to quick lime, it becomes calcium hydroxide also called slaked lime.
Do remember, when using lime in pickle making, the lime dust should not be inhaled. The lime-water solution is very alkaline. It is extremely important, for the safety of the processed pickles, that the multi-stage rinsing procedure for vegetables soaked in a lime solution be followed. The pH of the vegetables will increase during the soak, the acidity will decrease. It is necessary to get the pH of the vegetable tissue back down prior to pickling so the acid vinegar brine can do it's job of acidifying the vegetables enough for boiling water canning, to make them acid enough to prevent the development of botulism toxin.