The most interesting aspect of her life is arguably as a producer and studio head.
Biographies that focus on a specific aspect of a life, rather than the entirety, are often more interesting. Other than the "Red Scare" (already covered in BEING THE RICARDOS), Lucy's years as head of Desliu are probably the most narratively compelling for a film. I suspect most filmmakers would approach this devoid of nuance, and just portray Lucy as a powerful GirlBoss bitch. Her time as studio head was complicated. She was, by most accounts, quite competent in the role. She righted the studio after it had been floundering under Desi's final, drunken years. She ran the studio with enough of a creative open mind to allow adventurous shows like MISSION: IMPOSSIBLE and STAR TREK to be developed. All the while running and starring in her own top rated sitcom.
But she also hated the stress and responsibility of running the studio. She herself said that after particularly hard decisions, she would often go to her dressing room to cry. She faced frequent challenges from stockholders over the studio not being profitable enough. And the job seemed to acerbate her natural tendencies to be sociopathic, alienating her some of longtime colleagues (Vivian, her writers).
While a nuanced view of all of that could be an interesting film, I think we'd likely get an extended version of the MOMMIE DEAREST boardroom scene.