The aim of the study was to assess the fatty acid profile and nutraceutical properties of lipids contained in fallow deer (Dama dama) meat produced in organic and conventional farming systems. Longissimus lumborum (LL) and semimembranosus (SM) muscles from 24 fallow deer carcasses were selected for the study. The fallow deer meat from the organic farming system was characterized by significantly lower intramuscular fat content. The fatty acid profile in the organic meat was characterized by a particularly high proportion (p < 0.0001) of conjugated linoleic acid—CLA (LL—2.29%, SM—2.14%), alpha-linolenic acid—ALA (LL—4.32%, SM—3.87%), and docosahexaenoic acid—DHA (LL—2.83%, SM—2.60%). The organic system had a beneficial effect (p < 0.0001) on the amount of polyunsaturated fatty acids (PUFAs), including n-3 PUFAs, which resulted in a more favorable n-6 PUFA (polyunsaturated fatty acid)/n-3 PUFA ratio. The significantly higher nutritional quality of organic meat lipids was confirmed by such nutraceutical indicators as the thrombogenic index (TI), ∆9-desaturase C16, elongase, and docosahexaenoic acid+eicosapentaenoic acid (DHA+EPA) in the LL and SM and cholesterol index (CI), and the cholesterol-saturated fat index (CSI) indices in the SM. LL was characterized by higher overall quality.