Consider the lines \( L_1 \) and \( L_2 \) defined by
\( L_1 : x\sqrt{2} + y - 1 = 0 \) and \( L_2 : x\sqrt{2} - y + 1 = 0 \)
For a fixed constant \( \lambda \) , let \( C \) be the locus of a point \( P \) such that the product of the distance of \( P \) from \( L_1 \) and the distance of \( P \) from \( L_2 \) is \( \lambda^{2} \). The line \( y = 2x + 1 \) meets \( C \) at two points \( R \) and \( S \), where the distance between \( R \) and \( S \) is \( \sqrt{270} \) .
Let the perpendicular bisector of \( RS \) meet \( C \) at two distinct points \( R' \) and \( S' \). Let \( D \) be the square of the distance of the distance between \( R' \) and \( S' \)
The value of \( \lambda^{2} \) is _____
