Ingmar Guandique, 29, is to be sentenced Friday.
Prosecutors told Judge Gerald Fisher that Guandique "demonstrated predatory behavior that seems incapable of rehabilitation" and "posed a grave danger" to the community, The Washington Post reported.
Guandique was convicted in November of two counts of first-degree felony murder for the kidnapping, attempted robbery and killing of Levy.
The 24-year-old Levy disappeared in May 2001, and her remains were discovered in Rock Creek Park a year later. Guandique, already in prison for attacking two women in the park in the same period, was charged with the killing in 2009.
In their sentencing memo, prosecutors described earlier attacks by Guandique against women, going back to before he immigrated illegally from El Salvador. His attorneys are seeking a new trial.