Step 1: Understanding the Concept
Each crystal system has a fixed number of Bravais lattices.
Step 2: Counts
Cubic has 3 (simple, body-centred, face-centred). Tetragonal has 2. Orthorhombic has 4. Triclinic has only 1, the primitive lattice.
Step 3: Conclusion
Triclinic has the lowest number of Bravais lattices.
Final Answer:
The triclinic system has the fewest Bravais lattices.
\[ \boxed{\text{(C) }\text{triclinic}} \]