You are correct to be concerned about the lobbying issue.  In looking at your son’s website, it appears that the primary – if not the only – purpose of the organization is to lower the voting age in the state, an accomplishment that would require a change in legislation.  The IRS considers an organization that can accomplish its purposes only through a legislative change to be an “action organization,” which is not qualified for 501(c)(3) status. (See Ready Reference page: “IRS Has Generally Expansive View of 'Charitable.'”)  It may qualify, however, for 501(c)(4) status.  Contributions would not be deductible as charitable contributions, but it would not have to pay tax on any surplus income.

There may be another issue in the governance of the new nonprofit corporation.  Most state nonprofit laws require directors to be of “full age,” usually 18 years of age.  He may not be able to serve as a director of “his own” corporation.
By the way, I loved point 7 on his top 10 list of reasons to lower the voting age:  “If we let stupid adults vote, why not let smart youth vote?”