A velomobile is heavier and faster on the flat than almost anything.
but it's shite when climbing ....
most people (who are reasonably fit), can cycle 30Km/hr or a bit faster on flats when there is very little wind, irrespective of which road bike that they use (I'm not talking about hybris or MTB's etc)...
and I'm speaking from my own experience from owning several bikes
Hit the hills and this is where races are won ....
On a long Audax such as LEL, which is 1441km long and has 11,128m of climbing, a light climbing bike will gain you a lot of time with that elevation (especially if you are climbing into head wind) .... maybe enough time to finish the ride in time?
as for headwinds, I have owned a few light bikes such as a very light Specialized S-Works, (sad that I sold it) and it's a lot faster in headwind than many of my other heavier bikes (tested on several routes with the same wind direction and wind speed)