My Ellie is dog aggressive but only when she is on a lead, so it is worth bearing in mind that dogs can be worse if they are on a lead (ie they can't escape). Ellie isn't interested in other dogs but if they approach her when she is on a lead she will lunge for them, she barks continuously if they are too close. By contrast when she's off lead she is so much better, because she isn't interested in other dogs she tends to move away from them, however if they get too close to say her ball (most prized possession) she will go for them and it doesn't matter what size of dog.
She can be quite intimidating to other dogs and it took over a year to be able to train and run her successfully in flyball competitions. Now when we're at competitions we have to stand slightly apart for others and she seems fine when just walking on lead with others - ie, you need to keep moving as soon as you stop you can expect an outburst. I have yet to pinpoint why she reacts in the way that she does, but it does seem to be partly possessiveness over me I think and also her lead
though she doesn't seem to show any aggressiveness to dogs in her family just dogs she doesn't know.
Intially when she started competing she would aggressively chase after the dog that she would run into, but we've worked on that in training and discovered a dog running towards her at full pelt was scaring her so we started to feed her in from the side so that she couldn't see the other dog coming - gradually moving her to face the dogs head on, now she runs full on into other dogs without batting an eyelid, but I've only started doing that in the last month - she's realised that the other dogs don't want to hurt her, they're not interested in her.
I think what I'm trying to say is that it can take a long time, involve lots of repetition in calm and controlled environments and watching for triggers (which are often not easy to see). We still can't stand close to other dogs, but have noticed that her barking is different, not so aggressive but just general barking. As she is a rescue I don't know her background, but she has changed a lot in 2 years, for the better I think, its just taken a bit of time.
ETA: as Lilly's attack happened when she was on lead you may find that she will be worse when she is on lead.