Lineage is significant because Beowulf was written during a time when most stories were passed on orally.  Only the most essential religious, and some court/royal, documents were committed to writing. So, to preserve the history of a kingdom or a tribe, the stories had to often use an elaborate way of telling the stories: a way that is both entertaining as well as a record keeping.  When you hear texts (think Biblical and other epics such as The Illiad), there are often long passages chronicling "son of so and so, who begat this person, who reigned for a week," and so on.  Also, story-telling was not just a source of entertainment and historical record; it was a way to immortalize kings (in this world) and the heroic deeds done during their reign. There is a theme of loyalty to the king/lord in Beowulf, but also amongst the kingdoms during the time this epic was written.  So, those stories would often include homages to the king, (beotword) and to preserve the identity of the king himself, the story tellers had to repeat the lineage and therefore, lineages simply became part of the style of this type of literature.  Very characteristic of 'epic literature.'