It is not lawful to apply black hair dye. However, after applying hair-dye, if it gets a layer over hair, then it is unlawful to apply such dye of any colour. Wudhu and ghusl will not be valid with it, because it will prevent water to reach the roots.
It is lawful to apply hair dye other than black colour such as yellow and red etc which does not get layer.
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband