2. $\displaystyle \lambda$ is the normalization coefficient of the probability density function it's there to make sure that the p.d.f. is legal: The total integral of the p.d.f. must equal 1, which means that the sum of the probabilities that the r.v. is in some interval equals 1.
$\displaystyle \int\limits_{ - \infty }^\infty {\frac{\lambda } {{1 + \left( {x - a} \right)^2 }}dx = 1}$