The Big Lebowski is very high-brow, by the way. If anybody questions the academic merit of it, you can discuss how Oedipal it is (among other things).
One of the major things in Freud's Oedipus Complex is the son wanting to sleep with the mother. Consider when The Dude is introduced to "Mrs. Lebowski" ("Oh, you're Bunny.") -- she immediately offers to do sexual things. He's a Lebowski, she's a Lebowski. But she's married to an older, father figure ("Go get a job, sir!"), so she is at least somewhat introduced as a "mother figure" to The Dude's "son figure."
And then recall how The Dude in fact DOES sleep with another Lebowski -- Maude. Even though this would play into a sort of "sister" in my theoretical setup, there is still much parental tension displayed ("I'm sorry your stepmother is a nympho..." "Please don't call her my stepmother.").
To stretch this aspect a bit more, all The Dude ever wanted was to get his rug back -- a yearning to restore the status of his home ("It really tied the room together") -- possibly a display of getting his parents back together or trying to mend a broken home from his youth.
Another powerful aspect of the Oedipus Complex is displayed through the film's threats of castration -- this was a major part of Freud's theory too. The father would fear that the son would castrate him, in order to render him useless so that the son may take the father's place with the mother figure. The Germans threaten The Dude with castration and The Dude in turn threatens Larry with castration. (Neither of these come from a "son figure" wanting to castrate a "father figure", but the mere inclusion of the threats ties it in together with Freud.)