These synods are not affiliated with each other and vary in their doctrinal beliefs.
The following is a list of Lutheran elementary schools in the United States for which Wikipedia articles exist: This is a list of Lutheran high schools by state and city.
[1] Many North American Lutheran denominations have universities and seminaries affiliated with them.
The ELCA has schools which are part of the Network of ELCA Colleges and Universities while the Lutheran Church–Missouri Synod has the Concordia University System.
Valparaiso University is a Lutheran university that is not affiliated directly with a single denomination but shares ties to the ELCA and LCMS.