We studied this in school awhile back. Sometimes the procedure is put on hold at the very last minute (called a "stay of execution"), so they sterilize it just in case that happens. It's also a little more respectful to the inmate.
In nursing, we were taught to make our care client-centered. Also, we were taught to respect the dying and treat them with dignity. Sterilization of the needles means that even if the person is for lethal injection, we are still supposed to treat them the same way we treat other clients. It establishes respect for the client as well.
If they don't the human right activist will give them a beat down. If you ask me they keep people on death row for too long. If some one is convicted of murder beyond a reasonable doubt they should get lethal injection within the first month not 10~15 years down the road!
Because they still are trying to keep order even though they are "taking" a life. It's not really about preventing the person from being infected. Still though, I'm sure who ever does this would like to know exactly what they are injecting. Sterilizing keeps out other things, and keeps it simple. Nonetheless, I'm sure there are ethical reasons involved too, and there is no need to debate that as that would be a never ending debate.
I think it is merely medical procedures that all healthcare providers ought to follow. The reason for euthanasia is that it allows the person to die without pain and at least conserve a little dignity and grace. Having an infection that may cause bloating, bruising or some other unsightly stuff actually degrades the patient's dignity, which pretty much defeats the purpose of euthanasia in the first place.