Why does the U-2 Dragon Lady not have swept wings?
Sweeping a wing costs weight, for several reasons. Therefore, if the goal is to fly high and achieve long range, an unswept wing is the better choice. Only when transport performance needs to be maximized will a moderately swept wing look better.

Why is a swept wing heavier?


Sweep reduces aerodynamic efficiency, so a larger wing is needed to create the same amount of lift.
Sweep introduces torsion when a straight wing will mostly see bending only. Adding torsion strength needs more structure.
The stall characteristics of a swept, high aspect ratio wing are extremely unpleasant and require a healthy margin from the stall angle of attack, when flying high requires to fly just at the edge of stall. 


In the end, Kelly Johnson decided to cut weight and drag as much as possible but not to pursue maximum speed to achieve the greatest flight altitude. Another reason was that the U-2 begun as a modification of the XF-104 with extremely stretched wings. Adding sweep would had resulted in too many modifications to the U-2 fuselage, which was initially built in the same tooling than that of the XF-104.