There has to be volition to it, the Bible is clear that Jesus chose to lay down his life and no one made him do it.
The only questionable part is the eternality of an attribute dependent upon Christ's created status. From my experience most theologians do not consider Jesus to have eternally been a man, and I would agree. Since his manhood is necessarily connected to his sacrifice, I would consider there was a time he became a Lamb for us just as he became a man for us.
There is one interesting variant about the "Lamb slain before the foundation," but this has some questions marks surrounding it about the application of the "before the foundation" and where it should be, so it seems highly questionable. One other argument did seem plausible to me: God had said Adam would become like "One of Us" knowing good and evil, and only Christ has known evil in an experiential sense. This may argue for an atonement somehow enacted outside of the dimension of time and perhaps therefore integral to the very being of Christ; this leads to some strange time paradoxes, however. OT saints were said to look forward to the "better thing" and it does seem like Christ died within time as he came "in the fullness of time." However, how could blessings and coverings be dispensed pre-atonement, as if on a promissory basis? Yet, this seems to be the Biblical model, or the veil would have been made already rent. It could theoretically be both inside and outside of time in different aspects. I can't think of another verse indicating Christ died before creation, but would be interested in it. Of course his status or label as a "Lamb" is not necessarily connected to him having already died, but it does seem bound up with the idea, and only as a man could he be slain. Were he a "Lamb" within his eternality it feels like it would put creation logically and morally prior to God's existence, since the picture of the Lamb has no relevance without a fallen creation.
