Here's a summary of the case:
UK: We need the person responsible!
Libya: Here's a person!
UK: Is that the right person?
Libya: It's A person!
UK: We need the right person!
Libya: No you need a result for political reasons.
UK: Valid point, hand him over for conviction *cough* I mean trial, *lol*.
The case was due to be appealed before his release on compassionate grounds (totally no connection there).
His family are simply trying to clear his name and prove he was just a stooge for Gadaffi and the Blair government.
I was reading this thinking that's a good summary then I realised it was me who wrote it three years ago, holy necrothreads Batman xD