Spectroscopic techniques were carried out to identify the dyes used on the famous mediaeval Lady and the Unicorn tapestries kept in the Cluny Museum. Among the six tapestries, La Vue shows a colour variation between the front, which appears blue, and the back, which appears violet, on the Lady’s skirt. In the Middle Ages, it was common for the violet colour to be made with a blue dye bath (woad or indigo) followed by a red bath, which could be madder, cochineal, kermes, or orchil. Since orchil is known to be very unstable to light, its potential use in the original recipe was investigated and a study on this dye was performed. Contactless analyses (hyperspectral imaging in the visible-near-infrared range and UV fluorescence spectroscopy) were carried out on both the tapestry and mock-ups prepared following various mediaeval recipes. The investigation allowed for the identification of woad and orchil on the back of the tapestry, which was preserved from exposure to light. In addition, an ageing study elucidated colour degradation, revealing not only the different responses to light of different dyes but also the effect of specific dye preparations on light resistance. The experiments showed that the longer the maceration, the higher the light resistance of the dye. Furthermore, the red orchil colour fades faster than the woad.