Lycopene is a red carotenoid pigment found in fresh tomatoes. Several epidemiological studies show that the lycopene content of tomatoes and tomato-based products is related to a variety of health benefits due to its antioxidant activity, which is fundamental in treating cardiovascular diseases, slowing down cellular ageing and preventing some forms of cancer. Furthermore, several studies in the past few years have shown that by-products of tomato processing contain significant amounts of bioactive phytochemicals, including lycopene, that once extracted from the tomato skin could be used as natural antioxidants for the formulation of functional foods or as additives in food systems to extend their shelf life. The purpose of this study was to evaluate the extractive process of lycopene, starting from tomato skin waste, performing a cyclically pressurized extraction process or rapid solid–liquid dynamic extraction, using a Naviglio Extractor. This is an alternative approach to recent solid–liquid extractive processes that depends on diffusion and the pressure/de-pressure mechanism, which was considered to account for the driving force (convective effect) of the accelerated extraction of compounds contained in vegetables (or, more generally, solid matrices) and those not chemically bonded to the chemical structure of solids that are insoluble in the liquid extractant. The chromatographic analysis by high-performance liquid chromatography of the lycopene extract obtained showed a purity of more than 98% (w/w). Finally, a numerical simulation of the process was performed, obtaining useful information about the kinetics of the process (time history) as well as its mathematical description. The numerical simulation supports the validity of Naviglio’s principle.