Lyanna Stark: A Gift from Old Gods
In asoiaf, weirwood influences seem far less widespread than they are in some of GRRM's other tales (see A Song for Lya or And Seven Times Never Kill Man!). In this series, weirwood influences are far more subtle, and far more selective.
Rather than inhabit/control the conscious minds of every sentient being in proximity, in Westeros a weirwood might only indirectly influence the subconscious. Direct weirwood-influence comes, in asoiaf, only after one with the gift weds the trees. And "one
The wolf isn't a literal wight of Lyanna or of the mother wolf. At least, not in my mind.
The best way I can think of to explain it is another example pointed out by @GloubieBoulga a couple months ago: that Dolorous Edd is the "spirit" of Eddard Stark. The character shows up in the book shortly after Ned dies, and his first words are about the bones of the dead. He is completely unlike Ned in personality, but the things he says are things that Ned / The King of the Underworld would say. We