NO no. has to be oil free (you can wash your hair at night to have a little natural oil in your hair then dye the following morning, tho it won't really help much coz coloring your hair would damage it as it is). leave-on creams can be passed as okay before dye but oil won't cause the dye not to sTick to your hair. you could use hot oil treatment after if you like
Maybe you should go to a professional. I don't know what type of dye you will be using but there may be complications if you're using bleach since your hair is damaged, I don't think it will just become healthy overnight. That's all I know.