Scientist Dr. Peyton Westlake is developing a new type of synthetic skin to help acid-burn victims. He is frustrated with a flaw that causes the skin to rapidly disintegrate after 99 minutes. His girlfriend, attorney Julie Hastings, discovers the Bellasarious Memorandum, an incriminating document proving that corrupt developer Louis Strack has been bribing members of the zoning commission. Before she leaves, Westlake asks her to marry him, but she hesitates. When she confronts Strack, he confesses, but shows Julie what he's been planning: To design a brand new city which would create a substantial number of new jobs. He also warns Julie to keep her guard up as mobster Robert Durant wants the document.
Back at Westlake's lab, Dr. Westlake is conducting an experiment when the lights go out. Dr. Westlake and his assistant, Yakatito are astounded to find the synthetic skin is stable after 100 minutes. Westlake deduces that the synthetic skin is photosensitive. Their joy is short lived, as Durant and his henchmen show up and demand the Bellasarious Memorandum which Westlake knows nothing about. While searching for the document, Durant and his gang kill Yakatito. The gang then proceed to beat Westlake, burn his hands on a piece of machinery and dip his face in acid, disfiguring him. After they find the document, they rig the lab to explode, with Julie watching the explosion. The blast throws Westlake through the roof and into the river. Thought to be dead by Julie, who attends his funeral, he survives but is hideously burned. He is brought to a hospital and subjected to a radical treatment which cuts the nerves of the spinothalamic tract, so physical pain is no longer felt. However, he also loses his tactile sensation. Removing this sensory input gives him enhanced strength due to adrenal overload and keeps his injuries from incapacitating him, but it also mentally destabilizes him.
After mourning the loss of his lab and realizing how badly burnt he has become, Westlake re-establishes the lab in a condemned building, using digitization to create a mask of his original face. The process is long, and in the meantime, Westlake plots revenge against Durant and his men. He kills Durant's favorite henchman Rick, but not before forcing the latter to reveal the identities of those involved, along with their criminal activities. Westlake then studies his enemies in order to subdue and impersonate them. When his face mask is complete, Westlake manages to convince Julie that he is indeed alive, and that he was in a coma rather than dead. He is aware of Julie seeing Strack after his supposed death, and eventually confronts her, to which she responds that Strack only comforted her. Westlake does not tell Julie about his condition, but asks her various questions on whether or not she would accept him, regardless of his appearance. Westlake now has a full clock schedule: Making the skin last longer than 99 minutes, visiting Julie, studying his enemies and even mimicking their voice patterns. His next excursion has him impersonating Durant himself, causing confusion among the mobster and his henchmen.
The next time Westlake and Julie have a date at the carnival, an altercation causes Westlake to lose his temper and inadvertently reveals to Julie that there is indeed something wrong with him. She follows him as he flees (his 99 minutes were up,) and when she discovers that he was using masks to hide his true face, she calls out to Peyton that she still loves him regardless. Julie later tells Strack that she can no longer see him, and after discovering the Bellasarious Memorandum on his desk while he was on the phone, she confirms that Strack was collaborating with Durant the entire time. She tells him that Westlake is still alive, but Strack tells her that as long as he has the memorandum, no charges can be filed. When Julie leaves, Durant enters and is told by Strack to capture Julie and kill Westlake.
Westlake eventually succeeds in killing Durant and all of his henchmen (except for the one with the wooden gun leg whose fate is unknown). Westlake impersonates Durant one final time when he meets up with Strack and a captive Julie as Strack plans to make the city "one less attorney." Westlake's ruse is broken by Strack who fights him on an unfinished building floor 650 feet from the ground upon Strack unmasking him. When Westlake gets the upper hand, Strack calls his bluff by saying that killing him would not be something he could live with. Westlake then drops Strack to his death saying to himself: "I'm learning to live with a lot of things." Julie tries to convince Westlake that he can still return to his old life, but Westlake tells her he has changed on the inside as well as out, and can not subject anyone to his new vicious nature. In the final scene, he runs away from Julie as they exit an elevator, and is seen from behind pulling on a mask which, when he turns around, reveals the face of Bruce Campbell. During this scene, Westlake can be heard off-screen: "I am everyone and no one. Everywhere. Nowhere. Call me... Darkman."

Question: What did Westlake ask Julie to do before she left his lab before he was burned?
Answer: Marry him.
Alternative answer: To marry him