Let the number of lines per direction be $1$ as shown bellow:
Here $x,y,z$ depict the directions of the line.
$\eta_{laddoo} = 1$
$\eta_{mouse}= 0$
Add one more parallel line to each dimension $x,y,z$ as shown bellow:
Encircled points represent laddoo $\Rightarrow \eta_{laddoo} = 3$
and triangle enclosed by them represent mouse $\implies \eta_{mouse} = 1$
Similarly for $3$ lines in each direction
$\eta_{laddoo} = 6\quad (1+2+3)$
$\eta_{mouse} = 4 \quad(2^{2})$
As we continue we get a series which depends upon the no. of lines per direction $($let say $l)$
So, $\eta_{laddoo} = \frac{l\left ( l+1 \right )}{2}$
$\eta_{mouse} =\left ( l-1 \right )^{2}$
$\lim _{l\to \infty} \frac{ \eta_{laddoo}}{\eta_{mouse}} =1/2.$
So, $D:$ $1/2$ is the correct answer.