Recycling spent lithium-ion batteries offers a sustainable solution to reduce ecological degradation from mining and mitigate raw material shortages and price volatility. This study investigates using electrodialysis with selective and bipolar ion-exchange membranes to establish a circular economy for lithium-ion batteries. An experimental data set of over 1700 ion concentration measurements across five current densities, two solution compositions, and three pH levels supports the techno-economic analysis. Selective electrodialysis (SED) isolates lithium ions from battery leachates, yielding a 99% Li-pure retentate with 68.8% lithium retention, achieving relative ionic fluxes up to 2.41 for Li+ over transition metal cations and a selectivity of 5.64 over monovalent cations. Bipolar membrane electrodialysis (BMED) converts LiCl into high-purity LiOH and HCl, essential for battery remanufacturing and reducing acid consumption via acid recycling. High current densities reduce ion leakage, achieving lithium leakage as low as 0.03%, though hydronium and hydroxide leakage in BMED remains high at 11-20%. Our analysis projects LiOH production costs between USD 1.1 and 3.6 per kilogram, significantly lower than current prices. Optimal SED and BMED conditions are identified, emphasizing the need to control proton transport in BMED and improve cobalt-lithium separation in SED to enhance cost efficiency.