Successful prevention of lithium dendrite growth would enable the use of lithium metal as an anode material in next-generation secondary batteries. Mechanically stiff solid polymer electrolytes have been shown to prolong the life of lithium metal cells by partially suppressing lithium dendrite growth. A series of diblock copolymers of high modulus and molecular weight were synthesized, and their nanostructures and electrochemical properties were characterized as a function of polymer composition and lithium salt concentration, including measurements of the limiting current. X-ray tomography was used to observe lithium metal plating and cycling through these solid polymer electrolyte membranes under a range of electrochemical conditions. Insight into the interplay between electrochemical and mechanical properties, polymer microstructure, and lithium electrodeposition morphology will aid in the design of next-generation electrolytes.