To confirm perpendicularity of lines, calculate the dot product of their direction vectors and equate it to zero.
Line 1's direction vector is \( \vec{d_1} = \langle -3, -4, 3 \rangle \).
Line 2's direction vector is \( \vec{d_2} = \langle -3, 3, -\lambda \rangle \).
The dot product \( \vec{d_1} \cdot \vec{d_2} \) is computed as:
\[ \vec{d_1} \cdot \vec{d_2} = (-3)(-3) + (-4)(3) + (3)(-\lambda) \]
This simplifies to:
\[ \vec{d_1} \cdot \vec{d_2} = 6 - 12 - 3\lambda \]
For perpendicular lines, the condition is:
\[ 6 - 12 - 3\lambda = 0 \]
Further simplification yields:
\[ -6 - 3\lambda = 0 \implies -3\lambda = 6 \implies \lambda = -2 \]
Thus, the value of \( \lambda \) for perpendicular lines is:
\[ \boxed{\lambda = -2} \]