The bleach is for lifting the existing colour - in your case it will be lifting the dye out (which is why it might take more than one go), in my case its to lift the dark hair I have in my grey (hair is never actually grey in colour, it's either pigmented or not, and it just looks grey when dark and white colours are mixed).
Then once you have bleached you have a more uniform colour, and then you put the toner on to get it to the right tone. Dialight 9.11 isn't a 'grey colour' it's a very blue toned toner (if you look up Loreal colours, the first number if the level of lightness and the numbers after the dot are tones: 1 is blue, so 11 is a very blue tone which will cancel out orange and yellow - however, obviously blue mixed with yellow makes green, so this is why if you go very ashy it can make a green tinge - hence the advice to go to a hairdresser, it can be a bit of a gamble!) It depends on the colour of the hair after it has been lifted with bleach as well. Dialight needs to be mixed with a developer - I bought the specific dialight developer, and I bought it in the lowest volume I think as that was the advice if you are toning.
The bleach also needs to be mixed with developer, you can do 20, 30 or 40 vol. 40 vol is not recommended, it is very strong! Despite my dark hairs being very dark and needing a lot of lifting, I use 20 vol and leave it on for longer. Apparently low and slow is better for the hair. I'm not gonna lie, my hair does have some weakness and breakage (it's very short at the moment, although I am trying to grow it) and takes a lot of conditioning/protein but I think that would be the case if I got it done at a hairdressers as well tbh, because if you want very blonde hair when you are not actually very blonde, that's what happens.
If she is planning on going grey and this is just a transition, it could be worth going to the hairdressers as a one off. I only do mine at home because I don't want to pay however much to get my roots done when I could just do it at home, plus I hate going to the hairdressers!