I searched for any scientific evidence that lead from bullets harm trees. I could not find any harm from the lead (other then the obvious physical trauma). You probably would not want to eat the tree, but there is no evidence that lead in moderate or even heavy amounts will cause to the tree to die, or live a substandard life.
Trees can survive for long periods with a few bullets in them.
Last week, park officials found a new one — although fallen — with two bullets still embedded in its trunk 148 years later.
“The real witnesses to the battle . . . are still here,” John Heiser, Gettysburg National Military Park historian, said Tuesday, “even though they can’t talk to us. . . . They’re the last living witnesses to this singular event.”
Maintenance employees found the bullets in an old oak tree that had toppled on Culp’s Hill, southeast of town, the site of bitter fighting between Union and Confederate forces on July 2 and 3, 1863.
The discovery was made Aug. 4 as employees cut into the fallen oak tree, and their chain saw struck the bullets. The park said the tree fell about three or four years ago. The bullets were about 13 feet up from the roots, and the part of the tree where the projectiles were found was about 27 inches in diameter. Washington Post; Gettysburg battle bullets found embedded in tree By Michael E. Ruane August 9, 2011
There might even be a bullet in the 2x4 your house is made from. We can see from the image below a bullet does not appear to harm the growth near the injury site any more than knot or broken branch would.
Plants can and do absorb lead, thought it seems it is more significantly absorbed from air then earth.
Riihling and Tyler (1968) grew plants from roadside seed in contaminated soils obtained near highways. The plants contained only 5-10 ppm lead in the dry weight of the plant, whereas the same species of weeds that grew in the same soils along the roadside contained 68-950 ppm lead in the dry weight of washed samples. These data indicate absorption of lead from the atmosphere. Lead in the Environment: Tom Gray Lovering U.S. Government Printing Office, 1976 (pg 69
But lead does not travel through the tree to any great degree.
A solution of lead arsenate was formerly widely used in orchard to control pests... However a study of uptake of arsenic and lead by apple and apricot trees growing in such soil has found that though uptake occurs neither metal reaches levels which are danger to consumer health. Metal Contamination of Food: Conor Reilly John Wiley & Sons, Apr 15, 2008 (pg45)
Trees exposed to metric tons of lead, do absorb some, but no indications of harm to the trees from it.
The researchers'' survey found 11 metric tons of shot in the shotgun range and 12 metric tons of lead bullets in the rifle range. "These ranges are 10 years old. Most of the lead shot has accumulated on about four or five acres. Some shots have been into the woods, which cover hundreds of acres," Rimstidt said.
However some lead escapes, he said. "But we learned that it is absorbed in the top few inches of soil and does not migrate beyond that," Rimstidt said. "Lead is not very mobile. It does not wash away in surface or ground water."
Another finding is that there are large amounts of lead in the trees near the shooting range – but not in a large percentage of the trees, Rimstidt said. "If and when those trees are harvested, they would be contaminated with lead "Science Daily:Do Lead Bullets Continue To Be A Hazard After They Land?, Source Virginia Tech November 5, 2004
Trees can be injured by trauma, same as a person. An occasional euphemism is to say someone died of lead poisoning when shot and this may be what is meant by phrase quoted in another answer "Few of these trees survive today, though. Historians say most literally died from lead poisoning."
There is no doubt that lead in animal carcass is harmful for scavengers. (Not strongly related to points above but worthy of mention)
Most lead-core rifle bullets fragment into hundreds of tiny pieces when they strike animal tissue. Lead-tainted meat may become part of scavengers' food supplies when any of the following occur: a wounded animal escapes a hunting attempt, an animal shot as a pest is not retrieved from the field, or when gutpiles remain on the landscape after a hunt. Over the past 3 decades, California condor recovery efforts have brought to light how this lead pathway in the ecosystem can threaten even the very survival of a species.But as you will see, impacts extend to many other wildlife species also. National Park Service: Lead Bullet Risks for Wildlife & Humans