UPDATE (6/26): Other sources have come forward to clarify although Lord and Miller were indeed going off-script to create new dialogue and action, there is disagreement over whether they were adding humor.
One person with knowledge of the dispute said they were clashing with Lucasfilm over changes to the script made spur-of-the-moment during filming. But improvisation in this case does not always mean comedy, the source said.
If there was a genre the directors were trying to impose upon the Han Solo film, it was more of a western than screwball comedy, according to this source, who added that had Lord and Miller wanted to shift the tone to humor, they wouldnt have hired cinematographer Bradford Young, who is known for dramas like Arrival and A Most Violent Year.
Another individual close to the movie agrees it wasnt a question about how much comedy would be in the film. While there are many variations on the reason for the clash, the consensus now is that the filmmakers were encouraging significant improvisation from the actors, which some at Lucasfilm believed was shifting the story off-course. (End update.)