If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar vectors and $\lambda$ is a real number, then the vectors $\vec{a} + 2\vec{b} + 3\vec{c}, \lambda \vec{b} + \mu \vec{c}$ and $(2\lambda - 1)\vec{c}$ are non-coplanar for:

Since $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar, they are linearly independent. So the given three vectors will be non-coplanar iff the determinant of their coefficients with respect to $\vec{a}, \vec{b}, \vec{c}$ is nonzero. Their coefficient matrix is $$\begin{pmatrix}1&2&3\\0&\lambda&\mu\\0&0&2\lambda-1\end{pmatrix}.$$ Its determinant is $$1\cdot \lambda \cdot (2\lambda-1).$$ For non-coplanarity, we need $$\lambda(2\lambda-1)\ne 0.$$ So $$\lambda\ne 0$$ and $$\lambda\ne \frac12.$$ Thus the vectors are non-coplanar for all values except two values of $\lambda$. Matching with the options, this is $\text{(C)}$.