Lithium‐sulfur cells are attractive energy‐storage systems because of their high energy density and the electrochemical utilization rates of the high‐capacity lithium‐metal anode and the low‐cost sulfur cathode. The commercialization of high‐performance lithium–sulfur cells with high discharge capacity and cyclic stability requires the optimization of practical cell‐design parameters. Herein, a carbon structural material composed of a carbon nanotube skeleton entrapping conductive graphene is synthesized as an electrode substrate. The carbon structural material is optimized to develop a high‐loading polysulfide cathode with a high sulfur loading capacity (6–12 mg cm−2), rate performance (C/10–C/2), and cyclic stability for 200 cycles. A thin lithium anode based on the carbon structural material is developed and exhibits long lithium stripping/plating stability for ≈2500 h with a lithium‐ion transference number of 0.68. A lean‐electrolyte lithium–sulfur full cell with a low electrolyte‐to‐sulfur ratio of 6 µL mg−1 is constructed with the designed high‐loading polysulfide cathode and the thin lithium anode. The integration of all the critical cell‐design parameters endows the lithium–sulfur full cell with a low negative‐to‐positive capacity ratio of 2.4, while exhibiting stable cyclability with an initial discharge capacity of 550 mAh g−1 and 60% capacity retention after 200 cycles.