Turning Lists of Formulas Into Lists of Ordered Pairs

lst = {2 k x - 3 y, 3 y + 2 k z - x, 2 x + 2 y + 2 z, k y};

You can use Coefficient as follows:

Flatten[Coefficient[#, {x, y, z}]] & /@ lst

{{2 k, -3, 0}, {-1, 3, 2 k}, {2, 2, 2}, {0, k, 0}}