The markers had the word Penny blacked out and the word racist written above them on Thursday night.
The city's International Slavery Museum said it was not certain whether the street, which was immortalised in a song by The Beatles in 1967, was named after the 18th Century slave merchant.
A spokeswoman said "more research is needed" to clarify the name's origin.
City tour guide Jackie Spencer, who runs Blue Badge Tour Guides, said she was "absolutely livid".
"It's pure ignorance," she said.
"We've researched it and it has nothing to do with slavery. James Penny was a slave trader, but he had nothing to do with the Penny Lane area."
Local resident Emmett O'Neill, who has helped clean the paint from the signs, said he thought it was "an idiotic act".
"If you want something removed, there's ways and means," he said.
"Defacing Penny Lane signs isn't going to change a lot [and] it's the wrong way to go about things."
PBS explore the creation of the Beatles' Sgt. Pepper's with a new documentary, and Penny Lane video fully restored. watch below.Sgt.
“Paul made his very own payment to the partitioning of beats,” he states. “Hetakes Little Richard’s 8 also defeats to a bar and also makes them right into 4 also defeats in a bar, which is a music variation, I expect, ”
Sgt. Pepper’s Musical Revolution" is a look back at the creation, and ongoing influence, of the revolutionary 1967 Beatles album, “Sgt. Pepper’s Lonely Hearts Club Band.” When The Beatles stopped playing live in 1966, they suddenly had the time to pour all of their energy into writing and recording, creating an album that was a performance unto itself. Released in 1967, after what had been essentially a media blackout on what the band had been up to, the album was immediately a sensation and was recognized as a new chapter, not just in rock music, but in the history of all music.
Hosted by British composer and television presenter Howard Goodall, "Sgt. Pepper’s Musical Revolution" uses visually striking elements to conjure up the psychedelic world of "Sgt. Pepper," provide context for the culture of the day, and show how the album was a driving force within that culture. It also highlights how contemporary projects, like Beyonce’s “Lemonade," would be unthinkable today had The Beatles not completely upended the whole concept of what an album should be. And for the Beatles fan in all of us, the show reveals material that has been squirreled away for decades, known only to a handful of people at Abbey Road Studios, including recordings of studio chat, and isolated instrument tracks and vocals.
