This will guarantee the alignment with less work on the part of the user. The legend on Lambert Conformal Projections usually have two reference latitudes. The Lambert Projection is indeed drawn on a cone, but not this cone. It is very plausible and tempting to suppose that the map is drawn on the cone through the two latitude circles mentioned in the legend. In fact, this inaccurate misconception appears in a number of popular texts on maps.
Elementary trigonometry shows the half-angle of the secant cone is the mean of the two latitudes.
If the reference latitudes are 30 and 60, the cone half-angle would be 45. The half-angle of the Lambert cone is a more complicated question. In the case of latitudes 30 and 60, the cone half-angle comes out to 45.6897, slightly more than half a degree difference from that of the secant cone. If the Lambert Cone were positioned to pass through the 30 degree latitude circle, it would also pass through the 61.3794 degree latitude circle, not the 60 degree circle. Another plausible misconception that appears in a number of popular books.