West, of course, released an album called Yeezus in 2013, to great acclaim. But if Sheezus is indeed an incline of the Allen bonce to the all-conquering Chicago rapper, then the title's track chorus is a different sort of gesture entirely towards the female pop stars it namechecks: Rihanna, Katy Perry, Beyonce, Lady Gaga and Lorde.
Rather than a nod, they meet - or appear to meet (more of that in a minute) - two raised fists as Allen laces up her metaphorical boxing gloves and says she's preparing to get back in the ring. This comes after she claimed in 2009 that she was retiring from music to concentrate on having babies, carving a career in fashion and making jam.
"Second best will never cut it for the divas/Give me that crown bitch, I wanna be Sheezus," she sings. Some reviewers, meanwhile, have noted a line shortly before that which appears to say "Katy Perry's boring". It shows how little some reviewers listen to pop music. It's more likely that the line actually runs "RiRi isn't scared of Katy Perry's roaring", presumably a reference to Perry's 2013 chart-topper Roar. So while Allen may style herself as being back in the ring, the song's chorus isn't quite the "bitch-slap" it has been portrayed as. Allen is more commentator here than combatant - Harry Carpenter rather than George Foreman or Muhammad Ali, if you like. Sure the song is sly and wry and cheeky, but it isn't disrespectful.
That's not to say she doesn't bare her teeth elsewhere. Insincerely Yours namechecks supermodel Jourdan Dunn and tackles celebrity culture head on - "I don't give a f*** about your Instagram, about your lovely house or your ugly kids" - while URL Badman does the same for those teenage internet trolls who sit around in their pyjamas all day growling over their keyboards and planning a career writing those snarky picture captions they use in Vice magazine.
And of course there's Hard Out Here, Sheezus's lead single and a Top 10 hit on its release late last year. It's been hailed as a feminist anthem but, taken in conjunction with a now infamous video in which semi-naked black women jiggle and writhe and metallic helium balloons spell out "Lily Allen Has A Baggy P****", it's clear it functions better as satire than polemic. In other words, Allen has less in common with Aretha Franklin and more in common with spoof rappers The Lonely Island, authors of The Lego Movie's dumb but irresistibly catchy Everything Is Awesome. Lines like "If you can't detect the sarcasm, you've misunderstood" kind of prove the point.
That said, Sheezus the album is hardly a pop masterwork. Sure it's refreshing to be poring over the lyrics of something as unashamedly pop-orientated as this and finding examples of nuance and wit alongside words of three syllables and more.
But too often the swearing seems pointless - "Under cover, under the covers/My man is a bad motherf*****," she sings on L8 CMMR - and from start to finish it's musically uninventive.
On Our Time tells how two girls go out to party, with one character hymning her record collection and stating "I've got everything that came out on Def Jam".
From the join-the-dots pop-by-numbers production on much of the album you wouldn't think so. That's not to say Allen can't nail a catchy chorus, but there's nothing here any half competent music student couldn't knock up on GarageBand given a couple of hours. Sheezus is laugh-out-loud funny at points, but the greatest service producer Greg Kurstin has done is foreground Allen's lyrics in the mix.