Clean labelling refers to consumers’ desire for manufacturers to be more transparent in the way their products are made and sourced. Natural antioxidants (spices, herbs, fruits, or vegetables) have been proven to offer the same functionality as their synthetic counterparts, with the advantage of being label friendly and process compatible, maintaining meat quality and reducing food waste. Lamb meat has the challenges to have an intense flavour and fat composition to test the effectiveness of some of these natural antioxidants like hydroxytyrosol (HXT). The current paper was designed to test both natural (HXTo) and synthetic (HXTs) antioxidants using four lamb patty batches: one Control (C) (which included sulphites); a reference (R) sample (14.6% carnosic acid and 6% carnosol from natural rosemary extracts, 200 ppm); a sample containing synthetic hydroxytyrosol (HXTs, 99% purity, 200 ppm); and a sample with added organic hydroxytyrosol (HXTo, sample 7% purity from olive tree leaves, 200 ppm). A shelf-life study was carried out for 6 days at 4 °C, testing proximal composition and mineral bioavailability, pH changes, colour (by CIELab), total antioxidant capacity (TAC by oxygen radical absorbance capacity (ORAC)), lipid and protein oxidation (thiobarbituric acid reactive substances (TBARs) and thiol loss, respectively), volatile compound profiles (by HPC-MS), sensory evaluation, and microbiological growth (as total vial count (TVC) and total coliform count (TCC)). Results revealed that lamb burgers with added HXTs had better-preserved raw lamb meat in the test conditions, with reduced colour losses, lipid oxidation, and release of volatile compounds, the half the microbiological growth (TVC) of the Control, the best TAC, and significantly increased (p < 0.05) minerals bioavailability, while maintaining sensory acceptability. In summary, natural antioxidants are an adequate strategy for lamb meat burgers. Regarding HXTo, obtained from olives, the synthetic analogue is even more effective in terms of preservative and antioxidant activity, and in maintaining the nutritional value, sensory characteristics, and safety of food products.