It's describing something that started in the past (the body was there). 

And has continued up until now or the present time stated.

The choices are laid, lain, layed, lied, lay. Laid and layed are not actual verb forms.

Lied means to not tell the truth. Lay means to place something down as an action.

Lain is the past participle form needed to describe something that started in the past but affects the present

So to best capture the tense required - that the body has remained in the street for three continuous days - the verb form that fits is lain. 

The full correct sentence is: "The dead body of the armed robber has lain in the street for three days."