Then bake it in cake pans. Good grief.
Good grief, indeed. Did you look and that recipe? It is half ground lamb and half ground beef.
You can make it with any proportion of ground meats you want.
I think doing this will require at least one test run to be sure it works and can allow for tweaks. Hopefully you like it and can eat the first result so it is not a waste of food and money. It might take a lot of tests but I get there are limits to that for this.
You can also change the amounts of seasonings to your tastes.
Not too much tweaking, considering the price of ground lamb versus the price of ground beef.
@Czarcasm do you mean you want to cut the cooked lamb “cake” meat into different shapes and stack them appropriately to make a 3-D lamb shape?
Mix some ground lamb, finely ground, seasoned like you want. Use commercial bread crumbs(I believe they are drier) or panko. More eggs than you think. Mix it up pat it firmly in your sheet pans. Edge to edge. Fridge overnight. Then bake.
It will probably be slightly rubbery.
But it will cut and be able to be transferred to a serving dish to shape. And decorate, ice, and garnish.
Apparently there is an Easter tradition of baking a conventional baked flour cake in a mold to be shaped like a lamb. The OP proposes to reverse this by making a cake of lamb meat but shaped like a conventional round or rectangular baked flour cake.
No.
I want to make a ground lamb dish that looks, as much as possible, like a cake you would get from a bakery.
NOT in the shape of a lamb.
I think you’re on the right path with the bunt pan. Just add a bit more egg and crumbs to bind the lamb into a meat loaf and ice with a ketchup-based sauce.
How about cupcakes?
Ahh. I don’t believe it will ever come from a bundt pan in in one piece.
You might be able to finesse that.
I guess if I were to do this I’d get a spring form pan. And parchment paper to line it.
And wish you good luck. Take a picture. 
“Oven genius”? “Born to the ladle”?
Martha Stewart?
Julia’s Child?
As an alternative to a bundt cake pan, what about a spring form pan (like for cheesecake)? I’m guessing that the reason you don’t want to use regular round cake pans is because there is nowhere for the grease to drain? (Although you’d have the same problem with a bundt pan.) You might be able to loosen a spring form pan enough to hold the round shape but allow the grease to drain.
Or if you have some old cake pans you don’t plan on using anymore, you could perforate the bottoms with an icepick to let the grease drain out.
Also, what about hummus for the frosting?
Humans for the frosting? That is disgusting!
What’s that?
Hummus?
(Emily Litella) Nevermind.(/EL)
I just checked the website for Big Y Supermarket; ground lamb is $12 per pound, while ground beef might be a third of that. So yes, any experiments are going to cost you. But if you want this thing to taste good, I think you’re going to have to make at least one as an experiment. However, if the goal is simply to make something that looks like a baked cake, it isn’t. There is apparently a Netflix game show called Is It Cake? in which contestants try to bake a cake that looks like something else (a purse, a Doc Marten boot, etc.). I don’t think anyone cares what the cake tastes like and I think that’s also true of some over-the-top wedding cakes.
Very bland, Being authentic medieval, it had no spices but a single peppercorn for the eye, but there were mint leaves and a couple other herbs to liven it up. Ground lamb in aspic, with chopped mint, and garnished with mint.
So yeah…yucky (more texture than taste but really the whole thing…not great).
But authentic as hell.