No. Henna-based products will not lighten hair—zero harsh bleaching chemicals. The pigments will keep the hair its existing color or color darker (depending on color used). Some of the red shades (Pure Henna, Wine Red, Mahogany) may express on dark hair (dark brown to black), but expect the result to be subtle.
Some customers with dark hair (dark brown to black) like the subtle reddish halo that Pure Henna and Wine Red can kiss to their dark hair. And it generally will slightly improve over a few applications, although still subtle.