Addition of pickling lime to pickled vegetables may have several consequences.  I consulted several experts and sources for additional opinions.  When pickling lime is used to increase the crispness of pickles, and it must be completely removed.  In addition, pickling lime is highly basic (non-acidic) and can increase the possibility of botulism in home canned products.  For these two reasons, I would recommend discarding the pickled vegetables. Even though you refrigerated them, pickling lime is still present in the jars. In addition, if the pickled vegetables were processed in a boiling water bath, the presence of the pickling lime may increase the risk of botulism.  The best source of information is from the University of Wisconsin Extension blog by Barbara Ingham found at: http://fyi.uwex.edu/safepreserving/2013/09/18/safe-preserving-grape-leaves-alum-and-old-wives-tales/

Pickling lime, or calcium hydroxide, is available in some supermarkets and canning supply stores. Lime provides calcium, which combines with natural pectin in cucumbers to form calcium pectate, giving the pickles a firmer texture. Lime is a highly-basic (non-acidic ingredient). The pH of a saturated solution of calcium hydroxide is 12.4. Soaking cucumbers in a lime solution makes it less likely that added acid (vinegar) is sufficient to ensure a product with a safe pH (4.6 or less). Food grade lime may be safely used only if you follow three rules:

1. A lime-water solution is used as an initial soak for fresh cucumbers 12 to 24 hours before pickling. It must not be added to the final brine or pickling solution in the jar. Only food grade lime should be used, never agricultural or burnt lime.
2. Lime is added at a rate of no more than 2 Tablespoons per gallon of water in the soaking solution.
3. Excess lime is removed by rinsing cucumbers thoroughly. To remove excess lime, begin by draining the cucumber and lime-water mixture, trapping the cucumbers in a colander. Rinse cucumbers thoroughly with clear running water. Place cucumbers in a pot and add sufficient clean water to cover. Soak for 1 hour. Repeat draining, rinsing and soaking two more times, for a total of 3 rinses.