Step 1: Understanding the Concept:
Among the 15 lanthanoids (La to Lu), all are stable or nearly stable except one element which has no stable isotope.
Step 2: Recall the fact:
Promethium (Pm, atomic number 61) is radioactive. It does not occur in significant amounts in nature.
Step 3: Why the other options are wrong.
Thulium (Tm), dysprosium (Dy) and europium (Eu) all have stable isotopes and are not radioactive.
Final Answer:
Promethium is the radioactive lanthanoid.
\[ \boxed{\text{(D) }\text{Pm}} \]