Ben Ainsworth Dear Ben, 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.