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UPDATE: So how do you mitigate it?

There is plenty of advice in stuff up there that seems judgy or paranoid but actually engages some of these forms of risk.

• To make sure it is not a favoritism/pressure make sure there is no organizational power that can be contrived in an argument (or court) to show one is in executive authority over the other.
• To keep it from being a hostile work environment, take baby steps, and work on being aware of both how she reacts and how other folks in the lab react.
• To keep from being sued, be extra specially careful not to go anywhere near anything romantic until there is some strong and consistent-over-time trend toward acceptance and enough concrete evidence (not hearsay) to let you defend yourself in a court of law or even worse a brief university hearing in front of political sharks who would gut you for an ounce of push toward their next advancement.
• If it does get intimate, make sure you have both talked about and
  agreed upon the method of "protection" ahead of time, so that pregnancy does not become a disruption.
• Show enough consistent (and possibly expensive in terms of time or work) pursuit so that it is both widely obvious and any contenders can elect to join battle or forfeit in order to reduce human-level contenders.
• At some point, chat with a lawyer about liability and such. There might be free lawyers on campus that need volunteer work and could help you make sure you are not setting yourself on fire.

“Sonny, true love is the greatest thing in the world.” — Miracle Max, The princess bride

You approach it like a (dumb) guy and she reports it as hostile work environment, so you are ejected from the program, get a reputation that is public enough to destroy your career prospects, and you have to flip burgers for the rest of your life.  

It works well for a bit, you get romantic first, but then you act like a (dumb) guy and she reports it as sexual harassment, so you are ejected from the program, get a reputation that is public enough to destroy your career prospects, and you have to flip burgers for the rest of your life AND she can pursue suing both you and the university in civil court.

It works well for a bit, you get romantic, and she gets pregnant, and then you act like a (dumb) guy and she reports it as sexual harassment, so you are ejected from the program, get a reputation that is public enough to destroy your career prospects, and you have to flip burgers for the rest of your life AND she can pursue suing both you and the university in civil court AND you are paying child support for the rest of your life and bring that into any future relationship.  Or she has to drop out of the program. 

Someone could falsely report your relationship as professional conflict of interest where you get an unfair advantage.  or where Where she gets an unfair advantage.

If you have met and talked with any reasonably smart lawyer-ish people, this question itself should scare the holy carp out of you... they can destroy you forever in ways you can't possibly begin to imagine.

You approach it like a (dumb) guy and she reports it as hostile work environment, so you are ejected from the program, get a reputation that is public enough to destroy your career prospects, and you have to flip burgers for the rest of your life.

It works well for a bit, you get romantic first, but then you act like a (dumb) guy and she reports it as sexual harassment, so you are ejected from the program, get a reputation that is public enough to destroy your career prospects, and you have to flip burgers for the rest of your life AND she can pursue suing both you and the university in civil court.

It works well for a bit, you get romantic, and she gets pregnant, and then you act like a (dumb) guy and she reports it as sexual harassment, so you are ejected from the program, get a reputation that is public enough to destroy your career prospects, and you have to flip burgers for the rest of your life AND she can pursue suing both you and the university in civil court AND you are paying child support for the rest of your life and bring that into any future relationship. Or she has to drop out of the program.

Someone could falsely report your relationship as professional conflict of interest where you get an unfair advantage. or where Where she gets an unfair advantage.

If you have met and talked with any reasonably smart lawyer-ish people, this question itself should scare the holy carp out of you... they can destroy you forever in ways you can't possibly begin to imagine.

Let's add a third body. Her advisor. Her rival. A rival to her advisor who wants to attack the advisor using you and/or her as a weapon? Another student at your level who also has interest. How can they put gasoline on any of the above?

Someone could falsely report your relationship as professional conflict of interest where you get an unfair advantage.  Where she gets an unfair advantage.

If, and only if, you can navigate the potential hells then you can also insert your presumed "heaven" with the possible outcomes.

Let's add a third body, which could be any one of:

• Her advisor
• Her rival
• A rival to her advisor who wants to attack the advisor using you and/or her as a weapon
• Another student at your level who also has interest

How can they put gasoline on any of the above?

Someone could falsely report your relationship as professional conflict of interest where you get an unfair advantage.  or where Where she gets an unfair advantage.

If you have met and talked with any reasonably smart lawyer-ish people, this question itself should scare the holy carp out of you... they can destroy you forever in ways you can't possibly begin to imagine.

If, and only if, you can navigate a few of these "potential hells" then you can also insert your presumed "heaven" with the possible outcomes.