Unconventional lattice thermal transport and high thermoelectric performance in eight alkali-metal half-Heusler compounds <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mi>Mg</mml:mi> <mml:mi>X</mml:mi> <

Understanding the lattice dynamical behavior responsible for anomalous lattice thermal conductivity is crucial for the discovery and design of materials with intrinsically low lattice thermal conductivity, thereby enabling high thermoelectric performance. In this work, we employ the harmonic approximation, self-consistent phonon theory, and the self-consistent phonon theory including bubble diagrams (SCPB) to correct phonon self-energy and renormalize phonon frequencies at various theoretical levels. Based on different theoretical foundations, phonon transport behaviors of eight half-Heusler (HH) compounds are systematically calculated within the Wigner transport framework. Multivalley conduction band minimum with varying effective masses lead to the coexistence of high Seebeck coefficients and electrical conductivity. However, moderate spin-orbit coupling (SOC) significantly narrows the band gap, reduces valence band degeneracy, and flattens dispersion, strongly affecting electronic transport. In this study, (i) the SCPB method captures lattice thermal conductivity with minimal deviation from experimental values by including both particle-like and wavelike phonon contributions, underscoring the necessity of bubble diagram corrections in strongly anharmonic materials; (ii) a multidimensional analysis reveals the physical origin of distinct rattling-like behavior observed only in KMgAs, KMgSb, and RbMgSb among the studied HH compounds; (iii) a correlation between phonon bandwidth, phonon band gap, and phonon-phonon scattering is established, offering an efficient approach to qualitatively infer phonon lifetimes from the phonon spectra; (iv) even relatively small wavelike phonon contributions significantly affect the temperature dependence of lattice thermal conductivity; and (v) SOC significantly influences the electronic properties of HH compounds (35.7--$50.0%$), even without heavy elements, challenging the conventional belief that SOC can be ignored in materials lacking heavy atoms.