Lily never shaded Fad, she praised her. Lily Allen has been hip for nearly 10 years now. Sheezus is a better album than literally 99% of this sites faves. Beyoncé and Taylor Swift are trash (not relevant, but it needs to be known).
She was definitely shading Fad, I don't think it was in a malicious way though
She was obviously being sarcastic, she was mocking the media for their press during the ARTPOP era. Sheezus (song) is literally mocking FOMOs who hang about on fourms pitting woman against eachother.