On one hand, it would obviously attract lightning, being a tall-ish conducter it would attract it, but cars and the like are said to be (relatively) safe specifically because they direct lightning around you to the ground. I imagine it would be similar to that.
That’s wrong. Height is more important than material because air is a fairly good isolator, but electricity will always run the path of least resistance, which will invariably be the metal gazebo if they’re close enough.
That being said, a metal gazebo can also act like a Faraday cage. The reason why a car is safe is because it’s a metal cage, electricity will flow more easily through the metal than through you so you’re safe. Wood might be less conductive than you, so the path of least resistance might go through you, making it less safe. Also trees are alive and have water inside so they’re way more conducting than a wooden gazebo.
All of this being said, being near lighting when it strikes is not safe, as the electricity dissipates on the ground it creates massive electrical difference in the ground, and the least resistance path might be to go up your body and down the other side. Curiously if your feet are at roughly the same distance from the lighting strike you’re less likely to be electrocuted as the difference in electrical potential will be small, however if one feet is significantly closer than the other, as if you were running away from the lighting the electrical potential difference might be enough to kill you.
Not according to the USA National Weather Service:
Those two sentences are entirely unrelated. Just because lightning will strike wood under some circumstances has nothing to do with whether it’s more likely to strike metal.
A more definitive statement would be, “Lightning has been repeatedly observed striking metal objects, and those made of other materials, with equal frequency, provided the objects are of equal height and in the same general location.”