DC analysis of common-drain NMOS amplifier
For quick hand analysis, I would personally not include the impact channel length modulation. 

Knowing,
$$ V_{GS} = V_G - V_S\;\;\;\&amp;\;\;\; V_{DS} = V_{dd} - V_S $$ 

and that the drain current equals,

$$ I_D=k_n(V_{GS}-Vtn)^2(1+\lambda V_{DS}) $$

Since gate current of Q1 is zero the drain current is also,

$$ I_D = \dfrac{V_S}{R_S} $$

Put it all together as,

$$ \dfrac{V_S}{R_S} = k_n(V_G - V_S-Vtn)^2(1+\lambda (V_{dd} - V_S)) $$
and solve for \$V_S\$.