I know making sure she's well socialized with other dogs is your main concern, but for now, taking her around other dogs and where other dogs have been is just too scary. I don't think you're going to miss the window, that just might be when its easiest to do it. Think of re-homed/rescued adults that might have not come from the best situation, it takes time and patience but they get there eventually. Don't stress out yet.
Maybe you could start with introducing her to other situations first:looking out the car window or accompanying you into stores on everyday errands (in my area this isn't really aloud so I substituted fast food drive-thru windows-its a stretch but better than nothing). Just look for opportunities where she can be with you, and be out experiencing new things.
First, work on her manners. The most common is jumping up on people when they're excited to see them -well dogs can do this with other dogs too. Start teaching her its bad to jump on you, and later that can translate to "no jumping on other dogs". (BTW, our little boy was really bad about jumping in other dog's faces to give kisses.) Some other dogs will interpret jumping as aggressive/dominating, so your Lily might get hurt.
It sounds like you're itching to get her to a park and take her on puppy play dates. Work on leash training her, just around the house. Until she gets trained well, don't use a retractable leash (she can have her personal space when you guys are done with the lesson
).
Sounds like your doing well so far. There's plenty you can work on while waiting for her to be healthy enough to enjoy her social outings. So by the time you finally do get to play around other dogs, she'll be safer and a little more comfortable with the situation because you taught her some basics before "throwing" her into a new situation.
Hope this helps.