= Solution
For a neutral atom, count both the nucleons and the electrons. Protons, neutrons and electrons are all <fermions>, and exchanging two identical intact atoms produces the sign $(-1)^{N_f}$ from exchanging their fermionic constituents. An odd number gives a composite <fermion>; an even number gives a composite <boson>, consistently with the <Spin-statistics theorem>.
A lithium atom has three protons and three electrons. Lithium-6 also has three neutrons, giving $3+3+3=9$ fermionic constituents; lithium-7 has four neutrons, giving $3+4+3=10$. Therefore
$$
\boxed{{}^6\mathrm{Li}\text{ atoms are fermions},\qquad {}^7\mathrm{Li}\text{ atoms are bosons}.}
$$
The <composite statistics of neutral atoms> cannot be inferred from the <mass> number alone: counting only nucleons would classify the nuclei and give the opposite answers here. The atom's total <spin> includes its electrons as well as its nucleus.
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