But does having a gun and ammunition in the house contribute to lead poisoning?
It certainly can, but it doesn't have to.
There are two general principles to keep in mind.
1. The dose makes the poison. When people say things like: "There is no safe level of lead." then you know they are pursuing an agenda and not providing useful information. Of course there are safe levels of lead. Taking it to the extreme, 1 atom of lead is not going to hurt anyone. Obviously, at some level it's going to become toxic, but the idea that any at all will cause measurable damage isn't reality.
2. There are toxins all around us. Their existence isn't a problem as long as they don't get where they don't belong in quantities/concentrations that are too large. You can have all the lead you want in your house as long as you make sure it doesn't get into anyone's body except in very small quantities.
Even the medical field uses lead--but they don't eat it. It's used for shielding xrays, etc.
Also keep in mind that the heavy restrictions on the use of leaded gasoline, and other uses of lead have reduced blood lead levels dramatically in the U.S. They are currently around 15x lower than they were back in the 1970s.
All that to say that it makes sense to be informed on the topic and to use that information to take precautions when dealing with lead, especially around children and pregnant women.
Where you will get into trouble is if you pretend that lead exposure can't possibly cause any issues, if you intentionally ignore reasonable safety precautions, or if you don't take the time to educate yourself on the topic as it applies to you and your activities.