But that wasn't a extradition from the UK case. They were captured in Syria and not the UK. What the home secretary said to the US was (paraphrased) "We will not seek that they get extradited to be trialled in the UK for their crimes". Basically, "you caught them, they are yours".
The part about extraditing someone from the UK (and the rest of the EU iirc) must come with written assurances that the person will not be given the death penality is written into UK Law. To go against that would need either a change in the law or have the Home Secretary face legal repercussions of breaking the law whist acting as Home Secretary.
They would have to be 100% sure that the other country would abide by the terms. But lets say the US promised but then broke that promise once they were on US soil, then it would have wider effects on the extradition treaty with that country let alone any other relationship with that country. Would it be worth it to the US to burn the ability to extradite other people in the future for just one case?
And that is even if they are seeking such a punishment. As it stands right now, Assange is "only" charged with conspiracy to commit computer intrusion which carries a max of 5 years in prison.
Assange's legal team will make sure that other charges that may be added to the case in the future can not be given the death penality if his extradition does go though (Just because he has been arrested doesn't mean Assange doesn't have any rights to fight the extradition request.) see the case of Gary McKinnon who was facing 70 years but didn't get extradited https://en.wikipedia.org/wiki/Gary_McKinnon (Though in that case, it basically came down to he was seeing so much time in the US prison, he has ASD and depression that it was highly likely that he would of ended his own life then spend it in a US jail that it was deemed it would be against his human rights and the extradition dropped.).
