Step 1: Understanding the Concept
A living fossil is an organism that has changed very little over a long time and was once known mainly from fossils.
Step 2: The lobe-finned fish
The coelacanth (Latimeria) is a lobe-finned fish believed to be extinct, until a living one was caught in 1938.
Step 3: Other options
Cichlids are modern ray-finned fishes, Seymouria is an extinct amphibian-reptile link, and ichthyosaurs are extinct marine reptiles.
Final Answer:
The lobe-finned living fossil is the coelacanth.
\[ \boxed{\text{(A) }\text{Coelacanth}} \]