Concordia Historical Institute (CHI) is the Department of Archives and History of the Lutheran Church Missouri Synod. They are glad to assist in researching LCMS parish records. Concerning Lutheran genealogy, please keep in mind that there is no database of names of American Lutherans. Generally, research is based on information connected to a parish and/or a pastor.
Most Lutheran churches only keep records of official acts, such as baptisms, confirmations, weddings and funerals. The records usually are located at the parish where the act took place, unless it is disbanded. CHI can help you with genealogy if you have very specific questions and reliable information about a baptism, wedding, etc. However, there are charges for non-members of the Institute.
Popular brochures include "Researching at Concordia Historical Institute," "Researching the Lutheran Pastor at CHI," "Researching Your Lutheran Ancestor at CHI," and "Resources Outside of CHI." You may write Concordia Historical Institute at 801 Seminary Place, St. Louis, MO 63105.
In addition, Thrivent for Lutherans provides online exchange of genealogy information. Though not limited to the Missouri Synod, it is a place where individuals may start to make some contacts.