Lebensraum was not about annexing ethnically German neighbors. Lebensraum was about the "German race" needing space to thrive and, being superior, having a moral right and "biological necessity" to conquer that space and wipe out the "inferior races" currently inhabiting it.
You are correct; lebensraum did go hand-in-hand with Hitler's Grossdeutschland. I argue that the Anschluss (the annexation of Austria) was in Hitler's eyes a test of pavement for lebensraum: for an even greater Germany. China's reconstitution of half a century old territories is evidence of this same desire.
