Lara can unlock her inheritance with just a signature giving her all the money and resources she needs. So why does she pawn her necklace in Tomb Raider (2018)? If she finds her father then the death certificate can be declared null and void, after all.
Why does Lara pawn her necklace?
The answer is twofold.
She doesn't believe that her father's dead and as a result won't sign the papers. Because of this, Lara tries making her own way by working as a bike courier, taking college courses and being as independent from her father's empire as possible. If she signs those papers then she's admitting to herself that he's gone for good.
She sells the necklace to get enough money to travel to the remote island of Yamatai where she believes her father is, or at least some clue of where he is.
If she finds her father then the death certificate can be declared null and void, after all.
Eventually she did find her father but he later dies. Only then was she ready to sign the papers and use the resources he left for her to further his research.