I'll be quite honest, I don't know alot about trees. However, saying that I have seen quite a few trees die from repeatedly being used as a backstop for rifle and pistol shooting. I've actually been in situations where a tree had the road blocked and I used a pistol to cut the trees in two. Simple answer is yes if its repeated enough.
We have a few pine trees, (in the 12" - 20" dbh range), on the Deschutes National Forest that are killed by being targets just as you are concerned about.
But it isn't from lead poisoning. It is from not dozens but many hundreds of rounds and the eventual total destruction of that portion of the stem.
Think of a hand gun as a primitive axe.
Of all the recreational users we have. Shooters are the most disrespectful to their surroundings. Shooting signs isn't enough.
Regular hunters are often just fine. But those two groups don't necessarily cross-over.
Now what could be different for your oak is susceptibility to rot. (The pine trees here are in a very dry setting and suffer from very little rot). Maybe a scar or two opens up the interior to some form of rot and it takes the oak out over a several year period eventually. Look over similar oaks in the area and see if that could be a possibility.