Would there be a problem shipping Lead (II) Nitrate in an aluminum container?

Hmmm. There might be.

Nitrate is an oxidizing agent. Aluminum is easily oxidized -- but aluminum is quickly coated with a hard coat of aluminum oxide when exposed to the air. The aluminum oxide coating prevents further oxidation of the aluminum underneath.

Lead (II) might be able to get through the aluminum oxide (alumina) coat and might be able to react with the aluminum.

I'm not absolutely that there would be a problem. I'm just saying that there are probably better materials.