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NC State Extension Gardener Plant Toolbox lists Citrus x aurantiifolia for USDA hardiness zones 9a, 9b, 10a, 10b, 11a, and 11b, in full sun (6+ hours of direct sun) with well-drained, moist soil; it does not tolerate standing water, flooding, or shade.
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NC State documents it as native to southeastern Asia and as heat-, sun-, humidity-, and drought-tolerant once established, while remaining highly susceptible to lime anthracnose. It is not native to North America; it was cultivated commercially in the Florida Keys in the 19th century, the source of the "key lime" name.
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A strictly tender tropical/subtropical citrus — outside zones 9-11 it must be container-grown and overwintered indoors. Plotwright Heat Tier upper bound Extreme per ADR 0021, reflecting its tolerance of hot, humid subtropical summers; cold rather than heat is the limiting factor.