= Solution
The <separation of variables> solution with <Dirichlet boundary conditions> on the cuboid is
$$
\boxed{n=\sum_{p,q,r\geq1}a_{p,q,r}\sin\frac{p\pi x}{\lambda L}\sin\frac{q\pi\sqrt\lambda\,y}{L}\sin\frac{r\pi\sqrt\lambda\,z}{L}\exp\left\{\left[\gamma-\frac{\mu\pi^2}{L^2}\left(\frac{p^2}{\lambda^2}+\lambda q^2+\lambda r^2\right)\right]t\right\}.}
$$
The constants are fixed by the initial density through <Fourier sine series>. The fastest term again has $p=q=r=1$. When $L=2L_{\mathrm{crit}}$, its growth rate becomes
$$
s_{111}=\gamma\left[1-\frac1{12}(\lambda^{-2}+2\lambda)\right].
$$
Thus the precise condition for no exponentially growing term is
$$
\boxed{\lambda^{-2}+2\lambda\geq12,\qquad\text{equivalently }2\lambda^3-12\lambda^2+1\geq0,\quad\lambda>0.}
$$
For example, $\lambda=1/4$ gives $\lambda^{-2}+2\lambda=33/2>12$, while $\lambda=6$ gives $12+1/36>12$: either a sufficiently flat or a sufficiently elongated cuboid suppresses growth despite its unchanged volume. The function $\lambda^{-2}+2\lambda$ decreases to its minimum $3$ at $\lambda=1$, then increases without bound. Hence there are two positive threshold values, with growth only between them; equality leaves one stationary term and all other terms decaying.
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