Did Jyn really assume her father was dead/had been killed on Lah'mu, or had she actually heard the rumors saying her father worked for the Empire (the same rumors that caused Saw to abandon her)?
"Any idea where he's been all that time?".
"I'd like to think he's dead " Jyn answered "makes things easier." - Rogue One novelization, Ch. 2
Part of her did think he might be dead, because when they tell her the pilot has a message from him hers thoughts go into turmoil when she realizes they are telling the truth.
My father is alive. My father is a traitor. My father is building a weapon to destroy worlds.
Based on this I think it is safe to say she assumed her father was probably dead, better that than a turncoat.
She's certainly heard the rumours...
There's discussion of this in the 2017 novel Rebel Rising, which follows Jyn between the Rogue One prologue and the film proper. For example, it establishes early that Jyn knew (or, at least, believed) that her father had survived Lah'mu:
Saw glanced where she was looking and nodded grimly. A Star Destroyer hung in the blackness of space, the sun illuminating the underbelly of the ship.
They'd sent a Star Destroyer for her father.
Papa's on that ship, Jyn realized, her eyes widening. He was somewhere, somewhere there, just out of reach but so close.
Rebel Rising Chapter 2
More to the point, the novel reveals that Saw told Jyn about her father's supposed allegiances not long after picking her up:
"Galen Erso is working alongside Orson Krennic." Saw spoke in clear tones, enunciating each word, as if he knew the truth would cut her and it would be cleaner if he used a sharp razor rather than a dull blade. "Your father is working - knowingly - with the Empire. He reports directly to Imperial forces. He has made it entirely clear to my sources that he has chosen a side, and that side is the Empire."
Rebel Rising Chapter 5
This scene takes place at least a month after Jyn leaves Lah'mu, but likely not much more than that.
...but it's not clear whether she believes he's dead
There's evidence in the narration throughout the rest of the book that she never really suspects Galen's death; in fact, there's a point, when she's around 17 or 18 (so three or four years before Rogue One), where she briefly considers finding him, and living in the lap of Imperial luxury:
What would happen if she went back to her father? The Empire had killed her mother but just taken her father. He was their golden boy, and he seemed to relish that status. Could she be afforded the same luxuries he had been? Another apartment on Coruscant, another Mac-Vee, another chance?
Rebel Rising Chapter 37
In fact, the epilogue of the novel implies that Jyn is lying about believing her father to be dead:
"That's your given name, is it not? Jyn Erso? Daughter of Galen Erso." He paused. "A known Imperial collaborator in weapons development."
"I have no father," Jyn said, her words strong with the conviction she put behind them.
Rebel Rising Epilogue
However, this becomes inconsistent with Rogue One (both the film and the novelization) and the Visual Guide cited by Valorum, so it's hard to say which explanation is canon.
The film's Ultimate Visual Guide advises us that Jyn is of the opinion that her father is almost certainly dead.
For Jyn, it's the swapping of one prison cell for another. She cares not for the cause of the Rebel Alliance, and being briefed by their command while still in binders does little to sway her. Until, that is, she hears about her father, a man she had decided had died years ago.