Didn't the shepherds bring a lamb? Christina Rossetti hinted thus "In The Bleak Midwinter".
And the shepherds:-
So they hurried off and found Mary and Joseph and saw the baby lying in the manger. When the shepherds saw him, they told them what the angels had said about the child.
That's all there is - no gift of a lamb!
Aha, some will cry, "the wise men brought gifts."
Absolutely, but not to the baby Jesus and not to the cattle shed. And NOT on camels!
Gift giving has always been part of various celebrations; Christmas, Easter, Birthdays, Other Anniversaries, Weddings, Engagement, A New Baby etc. etc. but CHRISTmas adopted the idea for other pagan and social sources.
Christine Rossetti got one thing right however, "Yet what I can, I give Him - Give my heart."
If only it were a bit easier to fit the words to the tune, we might be able to sing with more meaning and commitment!