I travelled with Lufthansa with my bike several years ago and they operated this policy then. They handled it fine without any problems. It also meant I could cycle to Heathrow as I live nearby. I could also cycle from the destination airport without fiddling around with the bike. It seems to me this is the only sensible baggage policy with bikes, as if you're going touring and box it up you have to find somewhere to park the box while you go onward to your destination, or you find yourself carting it around on trains - often not a convenient process.
I have never found a bike bag which was a reasonable price which fitted my bike without almost dismantling it, something I don't like doing very much in places where I don't have a lot of tools with me. Mine in a sort of indestructible touring bike and will take knocks, though wheels will always be ready to buckle if a heavy case is dumped on them.
I have also hired a bike in Germany. No big problem with this but they seem mostly to have 'City Bikes' on hire. Prices seem to be from around 10 Euros a day. In 'cycling' areas like Munster it seems most bike shops will hire you something, some at even less.
I wish other airlines were as laidback about it as Lufthansa. A quick run through the various airlines policies indicate that there is little logic or reason behind their policies except Ryanair, of course, who just regard it as another way of lifting money from your wallet.
