Ans is option (C)
By using the two point form of equation of a straight line, (for the points $(-1,1)$ and $(5,7)$)
$y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\times(x-x_{1})$
By substituting the points in the given formula, we get the equation of the straight line as $y=x+2$
So, now the intersection point of $y=x+2$ and $x+y=4$ is $(1,3)$
Since the line $x+y=4$ divides the line $y=x+2$ in the ratio $\lambda:1$, we use the section formula to determine the value of $\lambda.$ (Ref: Section Formula)
$\therefore$ $\frac{\lambda(5)+1(-1)}{\lambda+1}=1$ $\Rightarrow$ $4\lambda=2$ $\Rightarrow$ $\lambda=\frac{1}{2}$