The present research studied the potential of a four-generation divergent selection (Pannon maternal rabbit lines) based on the total body fat content to create two rabbit lines with different meat attributes: a Fat line to deliver greater amounts of healthy fatty acids for newborns and infants, and a Lean line intended to provide lean meat for everyday consumption. Selection was based on the fat index calculated in 10-week-old live rabbits by means of computed tomography (CT). For each generation, 60 rabbits/line were fed ad libitum with commercial pellet from weaning (5 weeks) to slaughter (11 weeks). A total of 15 rabbits/line were randomly selected for meat quality evaluations: the longissimus thoracis et lumborum muscles (LTLs), hind legs (HLs), forelegs (FLs) and abdominal wall (AW) were analyzed for their proximate composition and fatty acid (FA) profile. FA contents were also calculated. Results highlighted that it was possible to obtain leaner meat for everyday consumption in most meat portions starting from generation 4 (7.93 vs. 11.9, 5.10 vs. 5.98 and 7.26 vs. 10.9 g of lipids/100 g of meat in Lean and Fat groups for the FLs, HLs and AW, respectively). The sole exception was the LTLs, which were not affected by the divergent selection. The total PUFA amount increased in FL and AW (p < 0.05) portions of the Fat line only, attributable to a greater n-3 amount (151 vs. 216 and 73 vs. 143 mg/100 g of meat in Lean and Fat groups for the FLs and AW, respectively).