Our aim was to characterize the organoleptic and nutritional properties of meat from suckling (one-month-old) and light (around three-months-old) lambs in local breeds on the Spanish Mediterranean islands, using meat from male lambs of the Mallorquina and Roja Mallorquina breeds. The lambs were kept with their mother at all times under an extensive management system and fed on mother’s milk until naturally weaned. In the Mallorquina breed, suckling lambs (n = 20) were slaughtered after weaning and the light lambs were bred using natural pasture (n = 20) or concentrate (n = 20), and the Roja Mallorquina light lambs were fed pasture and concentrate (n = 20). The pH, colour, texture, water-holding capacity, fatty acids, volatile compounds and sensorial attributes of the meat were analyzed. No differences in meat colour or texture were observed. The highest levels of non-desirable fatty acids were observed in lambs raised using concentrate. Light lambs showed a higher aldehydes content than suckling lambs. High notes of lactic acid and milk flavour were detected. Regardless of access to pasture or concentrate, continued access to mother’s milk during rearing influences the sensorial meat traits of these lambs, so we consider this type of management an optimal way of obtaining the traditional ‘Mediterranean lamb meat’.