This may be a little weird, but a little trick i do to lighten/brighten up the area under my eyes is using a light layer of a matte, cream colored eyeshadow with a fluffly blending brush to set my concealer!
It sets the concealer so it doesn’t crease but also brightens the area! You could also use a face powder that is a few shades lighter than you. :)
*the color pictured here that i use is MAC Blanc Type