'Clean' means nothing that would dirty the knife. So no dirty back ends, and if the weather is wet, no wet muddy bellies.
We clip lambs' backsides whenever they go, unless they are spotless and for our own use. Once the weather turns wet and the ground muddy, they'll get their bellies clipped before they go and will be kept on plenty of straw overnight before going.
You also need them empty before they go on the wagon - lambs with clean butts and bellies but grass in their tummies can be absolutely filthy at the end of a 30 minute journey

Ours are hungered overnight if they're going to our local abattoir; if they're going on a lorry to a distant abattoir then they'll have had hay in the morning, up until maybe three hours before they're loaded onto our trailer or the lorry. Sawdust on the trailer floor to soak up any wet.