I’ll echo and expand on Shoshana’s post above.
Jews who observe the laws of kashrut (dietary laws) do not eat dairy products (or anything that’s come in contact with dairy or dairy-derivatives) for a period of time after consuming meat. This means that there are a wealth of non-dairy desserts in most kosher cookbooks.
Also, if you are looking for packaged desserts, check for kosher supervision marks that do not say “Dairy” or “D” next to them. In particular, if you see the word “Pareve” (or some minor spelling variant), which means “neither meat nor dairy”, you can be quite sure that there is absolutely no dairy in it (it may have eggs). Some kosher certification marks simply omit the word “pareve,” so the unadorned mark implies “pareve.”
Many “non-dairy” foods, like soy cheese and Cool-Whip, may contain milk proteins like casein. If that’s what he’s allergic to, be careful.
I’ll also add that major brands of fillo dough and frozen puff pastry (which makes really easy desserts) are pareve. Here’s a quickie recipe with frozen puff pastry that makes a good appetizer, but with more sugar makes a great dessert:
Tomato tart
1 sheet frozen puff pastry dough, thawed
vegetable oil
1 or 2 tomatoes, sliced very thin
sugar
herbs to taste
Roll the dough out on a lightly floured surface to half its original thickness. Brush with oil. Layer the tomato slices to cover the dough, leaving a little margin (like a pizza crust). Sprinkle very lightly with sugar and herbs for an appetizer, more sugar to taste for dessert (and use “sweet” herbs like tarragon or basil). Bake as directed on the puff pastry package.
Sounds weird to have tomatoes for dessert, but trust me.
-Rick