There is a growing interest in using by-products rich in polyphenols, such as carob pulp (Cp, Ceratonia siliqua L.), as a dietary source of antioxidants for animals. This study assesses the effects of including Cp in lambs’ diet and meat display time (0, 7, 9, and 11 days) in modified atmosphere packaging on meat colour, fatty acid (FA) composition, tocopherol levels, and lipid oxidation values in the Semimembranosus muscle of 40 light lambs. The lambs were fed with concentrates supplemented with increasing Cp levels (0, 150, and 300 g/kg) for 45 days before slaughter. Metmyoglobin (MMb) and malondialdehyde (MDA) contents increased linearly with display time (p < 0.05), regardless of diet (p > 0.05). At 11 days of display, MMb (28 ± 0.8%) and MDA (0.6 ± 0.1 mg MDA/kg of meat) contents remained within the acceptable limits. The α-tocopherol content was lower in the 30% Cp group and meat (p < 0.05). Total saturated and monounsaturated FA contents (934 ± 64 and 823 ± 65 mg/100 g of meat, respectively) did not differ significantly among the groups. However, the meat from lambs fed with 30% Cp showed reduced levels of branched-chain FAs, while polyunsaturated FAs increased (p < 0.05) compared to the control lambs. The inclusion of Cp in the lamb’s diet, up to 30%, did not lead to meat deterioration and improved certain quality parameters, including a healthier FA profile. These findings highlight Cp’s potential as an alternative antioxidant source in animal diets.