Several studies have shown that volatile compounds are particularly well-suited for the authentication lamb diet by gas chromatography-mass spectrometry (GC-MS) analysis of adipose tissue. The aim of the present work was to use dynamic headspace-GC-MS to study the variations in the amounts of volatile diet tracers in perirenal fat (PRF) and caudal subcutaneous fat (CSCF) in lambs (n = 24) that were fed with concentrate and then allowed to graze for 0, 17, 51, or 85 days. Twenty-six volatile compounds were found to distinguish between the four diets (p < 0.05) in both PRF and CSCF. Of these diet tracers, 16 were found to be related to the pasture diet and increased at different rates according to the time spent at pasture (latency), while 10 were found in higher amounts in tissues of lambs fed with exclusive concentrate and exhibited different rates of clearance (persistence). Twenty-four of these discriminant compounds, including alkanes, ketones, terpenes, and 2,3-octanedione, were previously stated as pasture diet tracers in several earlier studies, suggesting their potential universality. All degrees of latency or persistence were exhibited by the pasture and concentrate diet tracers, respectively. A principal component analysis performed on ratios of selected diet tracers from both adipose tissues evidenced successful differentiation of the four feeding situations.