Hey Tegan,
At 2yo I think Aidyn had even less than 15 proper words...
I told myself that I would look into his speech if he had not picked up more by 2.5yo. Well now he is a bit over 2.5, and he is picking up new words so fast! The other day he learnt 4 new words in one day (grandma, OK, steamroller and crash), and he is now talking in 2 word sentences which is a big improvement. Although he is still behind for his age, I am not worried any more, as he is picking it all up at such a quick rate.
I would say to give Lily a bit more time, and continue to do what you are doing by reading to her and repeating the same words over. It WILL sink in eventually!
Maybe the first thing you can get checked is her hearing, just to make sure its all fine, but then I really wouldnt stress too much about it for a while yet.

Also when Aidyn was that age, he had a few words that were unintelligible, but if you listened closely, we learnt that these 'sounds' were his words for actual objects and things, ie, dummie, blankie, cuddle (although they sounded NOTHING like the word they were supposed to be!) so maybe if you can pick up on some of her own language it may help with the frustration on both your parts?