One significant difference between the Lutherans and Anglicans is the source of doctrine for each belief system. Lutherans view the Bible as their only source, while Anglicans base their doctrines on both the Bible and the teachings and traditions of earlier church leaders.
There are several branches of Lutheran churches that were created as internal schisms arose. The Lutheran Church--Missouri Synod is one of the more conservative branches, and they believe the Bible is perfect and inerrant. Anglicans believe that the Bible must be interpreted in historical context. This results in practical differences. For example, the Anglican Church, known as the Episcopal Church in the United States, ordains women as priests, while the LCMS does not allow women to become ministers.
Another significant difference between the Anglicans and all Lutherans is the concept of apostolic succession. This is the belief that the original apostles ordained the first bishops and priests. Those bishops then ordained other priests throughout the history of the church, so that each priest in the Episcopal or Anglican Church can trace their spiritual lineage to those original apostles. Anglicans believe that this is where priests get their authority and the ability to perform sacraments, such as baptism and communion. Lutherans do not believe apostolic succession is necessary because the authority to perform the sacraments comes from God.