Step 1: Recall the compartment contents. The anterior mediastinum normally houses the thymus, lymph nodes and possible retrosternal thyroid, sitting in front of the pericardium.
Step 2: Use the four Ts mnemonic. Anterior mediastinal masses are Thymoma, Teratoma, Thyroid lesions and Terrible lymphoma. That accounts for thymoma, lymphoma and thyroid tumor among the options.
Step 3: Find the exception. Neurogenic tumors grow from the nerves and sympathetic chain that run in the posterior mediastinum, so they are characteristic of the posterior, not anterior, compartment.
The nerve-derived tumor belongs posteriorly, making it the outlier.\[\boxed{\text{Neurogenic tumor}}\]