Wohoo! After reading a few things online and the book Control Unleashed, I decided to try Touch with Lily before she started to react to strangers. So on our way out of the dog park, whenever people approached I told Lily to touch my hand. She did it! And the best part is that she didn't react to the people or other dogs at all!
Obviously this was a one time thing but I'm hoping that she'll get a really good nose touch to the hand because this is how a lot of people approach dogs. So, when someone holds out their hand to her, she will touch her nose to them and not be so afraid. Let's hope that it works!