If the hair is extremely lightened and will not hold any toners that require peroxide, will FRAMCOLOR PURE PIGMENT PLUS last longer?

Yes!

FRAMCOLOR PURE PIGMENT PLUS is a must have color for overstressed/damaged lightened hair that will no longer hold oxidative color or color that requires peroxide. The acid pH closes the cuticle and traps color molecules in the most porous parts that easily lose color.