Essential oils/hair color

I plan to put some essential oils into an unscented sulfate-free shampoo and conditioner.  Will they affect the dye/color on my hair? 

It depends which oils you use.  There re certain oils that are better for certain colors of hair.  Can you be more specific?  Also is your hair natural or colored?

My hair is dyed dark brown.  It wouldn't bother me if the color lifted a little bit because I had to dye it dark brown (my natural color) to cover some bright red highlights.  I plan to use ylang ylang, palmarosa and lavender essential oils. 

Thanks for your help!