This is not quite correct. LLNL is a Federally Funded Research & Development Center (FFRDC) which is owned, as a facility, by the government, but managed and staffed by a non-profit contracting organization called Lawrence Livermore National Security, LLC (LLNS) under a contract funded by DOE/NNSA. The board of LLNS is made up of representatives from universities (California + TAMU), other scientific non-profits (Battelle Memorial Institute), and private nuclear ventures (e.g. Bechtel.) LLNS pays, with very few exceptions, staff salaries at LLNL, and they are not beholden to the government civilian pay schedule.
Be that as it may, a number of positions at LLNL, including many of those affiliated with NIF, require that candidate is a US person and is eligible for a DOE security clearance. A security clearance is not necessarily binary on being a US person, but a number of national-security related positions may require not only the clearance, but also that the candidate is a US person (or outright forbid foreign nationals.)
Edit: I'm Canadian, the question is rhetorical.