DETROIT—General Motors and a joint-venture partner plan to build an electric vehicle battery factory in Lansing, Michigan, their third such factory in the United States. The companies’ plans were revealed on Friday in documents posted on the city’s website. They say the plant would cost up to $2.5 billion and employ as many as 1,700 workers. The factory would be built on the site of GM’s Lansing Delta Township Assembly factory, which has been annexed by the city under a revenue-sharing agreement. A joint venture between GM and LG Energy Solution called Ultium Cells LLC would build the plant. The selection is a big win for Michigan, which missed out on three Ford Motor Co. battery factories and an electric vehicle assembly plant that were placed in Kentucky and Tennessee. The documents seeking Renaissance Zone and industrial tax breaks say the joint venture is obligating itself to investment and job …