I'm not very familliar with places other than Hawai'i, so I can only tell
you about the Hawaiian plants. The plants that you see growing on fresh
lava will depend on what sources of seeds there are nearby. For example,
if there is un-damaged forest nearby that is full of ferns, then there
will be a lot of ferns colonizing a new flow. In general, the plants that
are the first to start growing on Hawaiian lava flows are ferns and a type
of tree called Ohi'a. Depending on how wet the area is, the first of
these may appear only a few months after the flow has cooled. New plants
colonize pahoehoe flows much sooner than they colonize 'a'a flows.
Eventually, once soil has developed, just about any plant can grow on an
old flow.
Scott Rowland, University of Hawaii