My interpretation of this acerbic classic's opening two lines:
"So Sgt. Pepper [the album, Paul's brainchild] took you [the listening public] by surprise,
You'd better see right through that mother(f*****)'s [=Paul's] eyes."
So John begins with a "Let me tell you the truth about your beloved goody-goody Paul" to the music fans.
Thereafter, having invited us in as witnesses, he consciously switches the narrative directing it straight at/to Paul himself whilst we look on....
It's laced with all sorts of clever and viscious barbs, with John's trademark peerless vocals and that hypnotic, serpentine rhythm - even the snake-like hiss: "sleep at nightssssssss" hints at Paul's perceived (by John) underhand, sneaky attitude. How can you sleep at nights, Paul? How can you look yourself in the mirror? was what a wounded John seemed to be saying. Lennon always covered his pain with anger. But this was the early 70s and as we all know, there was a LOT of paranoia and bad blood around at the time. George and Ringo tended to side with John in seeing Paul as manipulative and selfish, secretively cutting publishing deals, re-polishing his tracks alone in the studio after sessions wound up, timing press announcements about the band's break up etc. Of course it wasn't really like that, but the long shadow of Klein was still very much in evidence.
I've never held this song against John. It's too glib to dismiss him as being nasty. At the time he (wrongly) thought Paul was being a c**t and didn't shy away (did he ever?) from spelling out the truth as he saw it. Remember when it seemed they'd "rumbled" the Maharishi? it was always left to honest John to blow the lid off these things ("Sexy Sadie"). Also, let's not selectively overlook the fact that it was Lennon's confrontational battering-ram determination (that same "nastiness"?) which smashed through those conventional barriers which would otherwise have prevented such a cheeky, provincial, unconventional group ever having made their big breakthrough back in deferential, forelock-tugging 1962.
I've never seen "Let Me Roll It" as McCartney's reply to be honest. In fact you COULD argue that "How Do You Sleep?" was in fact Lennon's reply to the pointed lyrical references in "Too Many People" from "Ram", which pre-dates "Imagine" by a few months and contains a few veiled needles of its own, with references to "going underground" (remember John & Yoko's support for Oz?) and "eating too much cake" (the chubby diet regime of Primal Scream therapy) etc...
They were daggers drawn back then.
Happily, this didn't last.