Will Directions Lilac dye work well on gingery bleached hair?

: / if it's still got hints of ginger in it, it will probably go a bit muddy (think painting and colour wheels--lilac and ginger-orange are almost opposite, so if you combine them it makes a brown).

It won't be a clear lilac, that can just about be guaranteed.  Your best bet would be to take your time and do some bleach baths to get it pale enough.

I agree - pastel and light colours tend to need around a pale lemon base colour to get close to the proper/normal colour result.  I think as squishy says you will get a brownish colour or even still stay ginger due to the light shade of directions lilac.  Do a Bleach Bath to bring the hair lighter and then try a strand test.  

I would try it and see.  I used a lavender over yellow/orange bleached hair before and it went silvery lilac.

It depends on the depth of colour. If it's not very very pale then it won't work. Like the people above have said it'll just turn brownish.

When I used lilac my roots werent lightened to the same shade as the rest of my hair, they were a honey blonde colour. The lilac took great to the platinum blonde but my roots didnt take at all really, it just made them a darker, more ashy blonde.

if your lucky, at most, it will just act as a toner.

I agree with what's been said, you need to lighten a bit more and tone. Then you should achieve the shade you want.