The answer is BOTH: There are distinct types of lightning strikes to earth that can travel in either direction - cloud-to-ground lightning and ground-to-cloud lightning. For each of these types of lightning, current flow and leader development can also take place in both directions.
Lightning starts inside of a storm cloud in the form of a bidirectional leader
with a positive end and a negative end. Both ends propagate and branch in opposite directions.
Fig. 1: A rendering of a lightning discharge after it starts and grows inside of a cloud. The bidirectional leader grows in opposite directions into regions of opposing charge. Here, the negative leaders are growing downward and the positive leaders upward.
For a negative cloud-to-ground discharge (the most common type of lightning striking the ground), the negative end of this bidirectional leader begins heading toward the ground. This stepped leader (the channel of ionized air) propagates downward. When the tip of the stepped leader approaches the ground, one or more upward-moving leaders initiate from the ground. The two opposide-moving leaders meet in midair, usually at a point about 300 feet or less above ground. When the stepped leader and leader meet, they provide a conducting path for charge flow, like a wire connecting the cloud and the ground. There is then a tremendous flow of current upwards through this established channel, brightly illuminating it.
This animation depicts the stepped leader descending
to meet the upward leaders extending from the ground, and the first and subsequent return strokes. This is an extremely slow-motion animation- the actual process takes only a small fraction of a second. AT RIGHT: Photo of cloud-to-ground lightning.
Fig. 2: From high-speed video of a cloud-to-ground strike near Trenton, Illinois: The stepped leader descends, followed by the bright return stroke in the last 3 frames.
Unlike cloud-to-ground lightning which starts inside the thunderstorm, a ground-to-cloud
lightning flash begins from a tall ground-based object and moves upward
. This type of lightning is common with strikes to towers and skyscrapers: read more
This animation depicts a type of upward-moving ground-to-cloud lightning striking a tall television tower. AT RIGHT: Photo of ground-to-cloud (upward) lightning striking a television broadcast tower.