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The least common cause of hypercalcemia associated with malignancies is the secretion of vitamin D analogues by the tumor. While various malignancies can lead to hypercalcemia through several mechanisms, one of the most well-recognized is the paraneoplastic syndrome where tumors secrete substances that affect calcium metabolism.

Generally, bone metastases are a prominent cause, as they lead to osteolysis, where bone tissue is broken down, releasing calcium into the bloodstream. Additionally, parathyroid hormone-related peptide (PTHrP) secretion mimics the action of parathyroid hormone, promoting calcium release from bones and increasing renal tubular reabsorption of calcium, making it a more common cause of hypercalcemia in malignancies.

Secretion of vitamin D analogues by tumors, while a possible mechanism (especially in lymphoproliferative disorders), is relatively rare compared to these other mechanisms. Tumor lysis syndrome typically leads to renal failure due to a rapid release of intracellular contents, including phosphate, rather than causing hypercalcemia directly. Thus, this makes the secretion of vitamin D analogues the least common cause among the listed options.