Does lightning strike from the sky down, or the ground up?
The answer is both. Cloud-to-ground lightning comes from the sky down,
but the part you see comes from the ground up. A typical
cloud-to-ground flash lowers a path of negative electricity (that we
cannot see) towards the ground in a series of spurts. Objects on the
ground generally have a positive charge. Since opposites attract, an
upward streamer is sent out from the object about to be struck. When
these two paths meet, a return stroke zips back up to the sky. It is
the return stroke that produces the visible flash, but it all happens
so fast - in about one-millionth of a second - so the human eye
doesn't see the actual formation of the stroke.
Source: National Severe Storms Laboratory
The reason is that when cloud-to-ground strike approaches the ground, the presence of opposite charges on the ground enhances the strength of the electric field and the "downward leader" strike creates bridge for the "return stroke"; this per the wiki page for Lightning.
Cloud to cloud and Intra-Cloud Lightning
Might be worth also noting that cloud-to-ground is not as common as Cloud to cloud (CC) and Intra-Cloud (IC):
Lightning discharges may occur between areas of cloud without
contacting the ground. When it occurs between two separate clouds it
is known as inter-cloud lightning, and when it occurs between areas of
differing electric potential within a single cloud it is known as
intra-cloud lightning. Intra-cloud lightning is the most frequently
Appears that ground-to-cloud is possible, though normally only a result of a man-made object creating "unnatural" electric potential, and is the least common type of lightning.