Step 1: Check whether the lines can meet:
Add the y and z coordinates. For line 1, $y + z = (3 - \lambda s) + (1 + \lambda s) = 4$ for every s. For line 2, $y + z = (1 + t) + (2 - t) = 3$ for every t. Since $4 \ne 3$, the lines never intersect.
Step 2: Use the coplanar condition:
Two lines that never meet are coplanar only if they are parallel. The direction of line 2 is $(\frac12, 1, -1)$, proportional to $(1, 2, -2)$. Line 1 has direction $(1, -\lambda, \lambda)$. Equating, $-\lambda = 2$ and $\lambda = -2$, which is option (C).
Final Answer:
$\lambda = -2$.
\[ \boxed{-2} \]