Mixing lime with sulfur is suppposed to increase the fungicidal properties and it causes a chemical change that allows the sulfur to penetrate the leaf tissue. This mixture is extremely toxic to mammals and can cause eye injury and skin irritation so if you use it you need to wear good protective equipment.
Rather than something like this, I've been debating whether to use this stuff for 30 plus years and have not really found a need to yet, I've found far less toxic ways to control the few problems I have. Black spot can be controlled with a mixture of 1 teaspoon of baking soda with a few drops of a light oil in 1 quart of water or mix fat free milk and water anywhere form a 1 to 10 to a 50/50 mix has shown results for different people and places. If either of these are sprayed early on every 7 to 10 days it should control Black Spot and present far fewer health problems for you.

Since black spot overwinters in lesions on the rose canes, a proper dormant spraying can go a long way to alleviating the problem later on in the year. Spray with the lime-sulfur, dormant oil, or oil and baking soda formula when you prune and before the new buds break in late winter or early spring (depending on your location).

Better yet, spray with commercial Bordeaux Mix from the garden center. That will get not only the black spot, but botrytis spores (sclerotia), as well. (Like you, I don't like to use lime-sulfur sprays.)