Based on this thread: Siehe auch: Bread and butter
, LEO's suggestion for "überleben," given as "to live out," doesn't make much sense. "Überleben" can be translated, variously, as "to survive" or "to outlive," both of which are given in LEO as well, but "to live out" (especially with the moniker "Amer." attached) is wrong for "überleben." In fact, the AE/BE consensus - though admittedly based on a limited "survey" of Leonites - is that it should be deleted from the options given in "überleben," especially since LEO already contains "to live out sth." for "etwas ausleben," which would be the correct translation.
I haven't offered any documentation here because I don't really think it's necessary; I think the facts and words speak for themselves:
überleben - to survive
jemdn./etwas überleben - to survive/outlive someone or something
to live out (sth.) - etwas ausleben