plot(lambda u:1, (-2, 2)) plots an horizontal line where y is constant (i. e. $y=1$).
Do you want a vertical line, where the same value of x of x corresponds to (infinitely) many values of y ? This by definition cannot be the representation of a function of x.
You can use a parametric representation of such a vertical line ; for example, parametric_plot([1,lambda u:u],(0,2)) will plot the vertical segment from (1,0) to (1,2).
You can also directly use the primitive line : line([(1,0),(1,2)]) will get the same result as before.