George Lucas already tried to fix Han Solo's "parsec" mistake with the Millennium Falcon way back in 1977, shortly after the first Star Wars movie released. In the first Star Wars movie, Han Solo boasted about the Millennium Falcon to Luke Skywalker and Obi-Wan Kenobi by saying it "made the Kessel Run in less than 12 parsecs." It's an iconic phrase that's rooted in the very core of Star Wars, and it was even brought up several years later in Star Wars: The Force Awakens.
But the problem was that Han Solo's Kessel Run record - not to mention the fact that he referred to a parsec as a measurement of time - didn't make sense. In Star Wars, as well as real-life, a parsec is a measurement of distance equal to about 19 trillion miles (3.26 light years). So how could someone calculate a record in speed by using a measurement of distance? This is a question the Star Wars franchise struggled with for years, and it was one that Lucas actually tried to answer right not long after A New Hope had released.
Related: George Lucas Explained Why Chewbacca Didn't Get A Medal In 1977
Once A New Hope was in theaters, Lucas began ironing out the rest of the Star Wars franchise over the summer in 1977 - and that meant discussing seemingly minuscule details that would later become bigger issues, such as Han Solo's use of the word "parsec" when referring to the Millennium Falcon. As explained in J.W. Rinzler's The Making of Star Wars, Lucas noted that Han Solo modified the Millennium Falcon so that he could travel the shortest possible distances.
"It's a very simple ship, very economical ship, although the modifications he made to it are rather extensive - mostly to the navigational system to get through hyperspace in the shortest possible distance (par-sect)."
What Lucas is referring to in The Making of Star Wars wasn't shown on-screen until Solo: A Star Wars Story in 2018. In that movie, while attempting to evade the Empire and go through the Kessel Run as fast as possible in order to reach Savareen before all the coaxium they have explodes, Lando Calrissian downloads L3-37's navigational system into the Millennium Falcon. Han Solo uses L3's navigational system to make short hyperspace jumps, thus traveling through the Kessel Run in the shortest distance possible - 12 parsecs.
While it took Lucasfilm over 40 years to explain - in-canon - Han Solo's "parsec" quote, it was something that Lucas was already thinking about in 1977. It's unclear, though, why he decided to record a parsec as a measurement of distance in his notes, but not in the movie. It could've been because Star Wars fans were already noticing that Han Solo's quote didn't make sense, but whatever it is, Lucas was well ahead of the game. It just took over 40 years to see it realized on-screen.
