Do Lutherans believe that the story of Adam and Eve and all the book of Genesis is to be taken as literal truth?
For individual Lutherans, it varies. For what the Lutheran Church teaches - the majority teach a literal interpretation. There are likely a few more "liberal" Lutheran Churches and possibly synods that reject a literal account, but I have yet to find any.
When you ask "Do Lutherans believe", you're asking something that can't truly be answered any other way. Some Lutherans believe in a literal interpretation of Genesis, some do not.
When it comes to official doctrinal teachings, you would still need to narrow this down further. But you can typically determine a particular Synod's interpretation by finding their website and statements of faith. Most typically reject evolution and pronounce a belief in God's word as the ultimate source of Truth, and therefore stand by a literal interpretation of Genesis.
For example, the Missouri Synod says this:
We teach that God has created heaven and earth, and that in the manner and in the space of time recorded in the Holy Scriptures, especially Gen. 1 and 2, namely, by His almighty creative word, and in six days. We reject every doctrine which denies or limits the work of creation as taught in Scripture. In our days it is denied or limited by those who assert, ostensibly in deference to science, that the world came into existence through a process of evolution; that is, that it has, in immense periods of time, developed more or less of itself. Since no man was present when it pleased God to create the world, we must look for a reliable account of creation to God's own record, found in God's own book, the Bible. We accept God's own record with full confidence and confess with Luther's Catechism: "I believe that God has made me and all creatures."
Do lutherans believe in a literal interpretation of Genesis?
In addition to the Missouri and Wisconsin synods, the Lutheran Brethren also follow a literal interpretation