Lignin is C31H34O11, all stuff that the tree can get from air and water, so you've got a point there.
But a tree trunk is more than just lignin. Also it could be more complex than whether you're robbing the soil of nitrogen and phosphorous. There's a lot we don't know about the role of soil microbiota, for instance. I don't have any evidence that it's going to be a problem, but nobody has evidence that it's not going to be a problem either (only that it hasn't yet).
Although I guess this is all orthogonal to whether, once you've harvested the wood by whatever means, you process it into something stronger and denser.
But a tree trunk is more than just lignin. Also it could be more complex than whether you're robbing the soil of nitrogen and phosphorous. There's a lot we don't know about the role of soil microbiota, for instance. I don't have any evidence that it's going to be a problem, but nobody has evidence that it's not going to be a problem either (only that it hasn't yet).
Although I guess this is all orthogonal to whether, once you've harvested the wood by whatever means, you process it into something stronger and denser.