  Lattice thermal conductivity ($\kappa_{\rm L}$) is a crucial characteristic
of crystalline solids with significant implications for practical applications.
While the higher order of anharmonicity of phonon gas model is commonly used
for explaining extraordinary heat transfer behaviors in crystals, the impact of
exchange-correlation (XC) functionals in DFT on describing anharmonicity has
been largely overlooked. Most XC functionals in solids focus on ground state
properties that mainly involve the harmonic approximation, neglecting
temperature effects, and their reliability in studying anharmonic properties
remains insufficiently explored. In this study, we systematically investigate
the room-temperature $\kappa_{\rm L}$ of 16 binary compounds with rocksalt and
zincblende structures using 8 XC functionals such as LDA, PBE, PBEsol, optB86b,
revTPSS, SCAN, rSCAN, r$^2$SCAN in combination with three perturbation orders,
including phonon within harmonic approximation (HA) plus three-phonon
scattering (HA+3ph), phonon calculated using self-consistent phonon theory
(SCPH) plus three-phonon scattering (SCPH+3ph), and SCPH phonon plus three- and
four-phonon scattering (SCPH+3,4ph). Our results show that the XC functional
exhibits strong entanglement with perturbation order and the mean relative
absolute error (MRAE) of the computed $\kappa_{\rm L}$ is strongly influenced
by both the XC functional and perturbation order, leading to error cancellation
or amplification. The minimal (maximal) MRAE is achieved with revTPSS (rSCAN)
at the HA+3ph level, SCAN (r$^2$SCAN) at the SCPH+3ph level, and PBEsol (rSCAN)
at the SCPH+3,4ph level. Among these functionals, PBEsol exhibits the highest
accuracy at the highest perturbation order. The SCAN-related functionals
demonstrate moderate accuracy but are suffer from numerical instability and
high computational costs.
