If I got your question right, you want to draw something like a stairs. I will assume that one of the lines has an equation
a x + b y + c = 0 with nonzero a and b (special cases a=0 or b=0 are trivial). I will also assume that a^2+b^2=1 (if not, just divide the equation by 1/sqrt(a^2+b^2)).
Then if have the lengths of your lines L, and the coordinate of starting point is (x0,y0), then coordinates of other points, where perpendicular lines start are
(x_i, y_i) = ( x0 + (b L i)/(N-1), y0 - (a L i)/(N-1) ) where i runs fro 0 to N-1, and N is the number of points, that you need for your staircase.
Note: if points will go in the wrong direction, use the opposite sign
(x_i, y_i) = ( x0 - (b L i)/(N-1), y0 + (a L i)/(N-1) ) After you have points, where the perpendicular lines start, the parametric equations for each perpendicular line is
x_i(t) = x_i + a t D, y_i(t) = y_i + b t D where t changes from 0 to 1 and D is the distance between your parallel lines.
Note: if perpendicular lines go to the wrong direction, change sign
x_i(t) = x_i - a t D, y_i(t) = y_i - b t D That is more or less it)