Little Richard's place as one of the absolutely essential, seminal founding fathers of rock n' roll is unassailable. But that placement isn't made any more secure via imaginary narratives at the expense of other badass legends. That's to say, Jerry Lee Lewis didn't steal shit.
Of course, Jerry Lee Lewis is a bit of a thief. Just like Little Richard and every interesting artist ever. Both men played the piano. Both were incendiary personalities. Both emerged in the 50s. But it diminishes both Little Richard & the Killer to say they have the same act.
They worked different sides of the street. Little Richard's sound emerged from the black gospel tradition and from the jump blues, r&b sound of pioneers like Louis Jordan and Johnny Otis. But his flamboyant, androgynous, code-mixing personae was pure vaudeville.
Like many black singers of the period, Little Richard also had a kinship with hillbilly music. You couldn't swing a cat around a 1950s recording studio w/o hitting a badass artist mixing white & black textures together. Go on back to the '20s w/ Jimmie Rodgers, Louis Armstrong...
Little Richard's love of countrified forms -- & his genius facility with them -- comes to the fore in his album SOUTHERN CHILD, recorded in 1972 and unreleased for 30+ years. It's not straight country at all. It's pure Little Richard, but different:
Jerry Lee Lewis' sound also came out of the church, but with a deeper grounding in hillbilly music -- famously, his cousins were piano playing evangelist Jimmy Swaggart & country star Mickey Gilley. 
Like Elvis & Johnny Cash & Charlie Rich & Carl Perkins & every other interesting white singer of the era, Jerry Lee was deeply influenced by black music. Like how geniuses like Al Green, Bobby Womack & the Staples synthesized the influence of Hank Williams, the Carter family, etc
Jerry Lee's biggest stated influences were Jimmie Rodgers, Hank Williams, & Al Jolson. An interesting mix. What Jerry Lee valued in them was their interpretive prowess, their ability to personalize the songs via their unique styles and personae.
Jerry Lee had none of Little Richard's playful, flamboyant, subversive mixing of gender and sexual norms. Jerry Lee's entire persona was that of the doomed maniacal holy roller, the man who is terrified he's destined to eternal damnation because of his music but still can't stop.
If anything, to my amateur ears I think Jerry Lee's act actually had more kinship with Chuck Berry's in terms of its velocity, muscularity, adrenalinized masculine thrill seeking.
But even then, Chuck Berry didn't have Jerry Lee's perpetual spiritual inner civil war, which is the most enduring element of Jerry Lee's entire persona. It's that spiritual volatility that is so unique to the Killer.
I love both Little Richard and Jerry Lee Lewis. Bonafide geniuses and rock n' roll Greek gods. But to say that Jerry Lee stole Little Richard's act is to reduce both of their "acts" to being loud guys on the piano. And both men were so, so, so much more than that.
And I won't even get going on the Chuck Berry and Buddy Holly and Carl Perkins and Everly Brothers erasure one has to perform in order to reduce the early Beatles to just playing Little Richard songs...
It's pointless to try and correct strangers on the internet, but it's also weirdly torturous to see such a blatantly false narrative about artists you love get retweeted thousands of times because, I guess, it fits a certain simplistic contemporary template.
I'll end by posting two electrifying early 70s performances by Little Richard and Jerry Lee Lewis. Other than the piano, I can't imagine anyone saying they're the same act. It's like saying Prince and Kurt Cobain have the same act becuz they're both pretty dudes playing guitar.
