As Li-ion batteries are increasingly being deployed in electric vehicles and grid-level energy storage, the demand for Li is growing rapidly. Extracting lithium from unconventional aqueous sources such as geothermal brines plays an important role in meeting this demand. Electrochemical intercalation offers high Li selectivity and avoids the use of harsh chemical regenerants, thus holding great promise in directly extracting lithium from unconventional sources. In this work, we design an integrated electrochemical process that achieves selective lithium extraction from geothermal brine, purification of lithium chloride, and conversion to lithium hydroxide. The lithium extraction process utilizes a lithium-intercalation electrode, LiFePO4 (LFP), as the working electrode coupled with an activated carbon electrode as the counter electrode. A 91% purity LiCl is extracted from simulated Salton Sea geothermal brine containing 42 mM Li+, 3.1 M Na+ (Li/Na molar ratio 1:74), 1070 mM Ca2+, and 540 mM K+, and a further purification step achieves a pure LiCl solution with no Na detected. Subsequently, lithium hydroxide is further produced through a bipolar membrane electrodialysis system and finally crystallized to obtain battery grade (> 99.5% purity) LiOH•H2O solid. We investigated the selectivity of lithium separation in solutions with different cation concentration ratios as well as in synthetic geothermal brines. We further conducted density-functional theory (DFT) calculations to elucidate the mechanisms underlying the high Li selectivity of olivine FePO4 in aqueous solution. Finally, we conducted techno-economic assessments using a parametric model and estimated the levelized cost of produced LiOH•H2O (LCOL) as 4.1 $/kg LiOH•H2O, which is 6 times lower than the current market price. The results demonstrate the great potential of our technology for electro-driven, chemical-free lithium extraction from unconventional sources.