The shortage of some ingredients and, consequently, the continuous increase in the price of feed encourage the search for other alternatives to maintain animal production and enhance its products. In this line, the use of aromatic plant by-products in animal diet has been recently and widely considered, given their richness in bioactive compounds. Therefore, the aim of this study was to investigate the effects of the inclusion of rosemary residues (RR) and protein sources on lamb meat quality. The experiment was carried out on 24 male Barbarine lambs (3 months old) with an average body weight (BW) of 17.8 ± 2.6 kg, which were divided into three homogeneous groups according to BW. The diet comprised 600 g of oat hay and 600 g of concentrate. Three types of concentrate were evaluated: commercial concentrate as the control group (C); rosemary residues (RR) plus soybean meal as the RRS group, and RR plus faba bean as the RRF group. After an experimental period of 65 days, lambs were slaughtered. The inclusion of RR in both concentrates increased the α-tocopherol and total polyphenol content in meat and protected meat against discoloration (high red index and chroma after 9 days of storage) but did not affect meat lipid oxidation, which was similar for all groups. The FA profile was affected by the inclusion of RR, with no effect from the source of protein (faba bean or soybean). The inclusion of RR in the concentrate increased the C18:2 n-6, C18:3n-3, C20:4 n-6, C20:5 n-3, and C22:5 n-3 content (p < 0.05). Consequently, the inclusion of RR also increased the total polyunsaturated FA (p < 0.05) and the ratio of polyunsaturated FA to saturated FA (p < 0.05). The results of this study demonstrate that concentrate based on RR could be useful for lamb meat production by improving the nutritional quality of meat, especially the fatty acid profile. In addition, soybean meal can be replaced by faba bean in lamb concentrate without affecting meat quality.