A post at Cake Wrecks featuring the pictured cake of a lamb with a cigarette in its mouth led me to a previous collection of such cakes, which led to a post about the possible meaning of what appears to be a tradition, although not common enough to be well documented. Lamb cakes are baked for both Passover and Easter, and sometimes for a Catholic child's First Communion. The blog Romantoes gathered several theories from commenters.
* It's Joe Camel.
* The lamb is smoking to signify the end of Lent, and the enjoyment of vices one might have given up for Lent, such as smoking.
* The cigarette is supposed to represent a paintbrush, and is colored on the end to suggest the lamb's blood that was used to paint door frames during the original Pesach.
* What looks like a cigarette is actually a scroll, and is in the lamb's mouth to illustrate a passage from Revelations: "Then I saw, between the throne and the four living creatures and among the elders, a Lamb standing as if it had been slaughtered, having seven horns and seven eyes, which are the seven spirits of God sent out into all the earth. The Lamb went and took the scroll from the right hand of the one who was seated on the throne."
I looked around at forums that discussed the matter, but no one knew with authority what the "cigarette" meant. However, a few people mentioned that they had seen such lambs for sale at Jewish delis, which leads me to think the third explanation may be the one. Link
(Image source: Cake Wrecks)