Are sectional paths correct across "long" distances?

No. Straight lines on Lambert Conformal maps are not great circles.

It's my understanding that the Lambert Conformal is better than any
other flat surface at representing the curved surface of the earth in
such a way that a straight line on the chart comes very close to being
a Great Circle.

Any straight line through the exact center of a chart, regardless of
direction, will be precisely a Great Circle. A line across a corner
of the chart will be the poorest representation of a Great Circle, but
still "good enough for government work." Probably as close as the
average GA pilot can hold a course, anyway.

vince norris