The influence of micro/nanostructure on thermal conductivity is a topic of great scientific interest and of particular technological importance to thermoelectrics. The current understanding is that structural defects primarily decrease thermal conductivity through phonon scattering where the phonon dispersion and speed of sound are fixed when describing thermal transport, especially when chemical composition is unchanged. Experimental work on a PbTe model system is presented which shows that the speed of sound linearly decreases with increased internal-strain. This softening of the materials lattice completely accounts for the reduction in lattice thermal conductivity, without the introduction of additional phonon scattering mechanisms. Additionally, we show that a major contribution to the reduction in thermal conductivity, and the resulting improvement in thermoelectric figure of merit (zT > 2), in high efficiency Na-doped PbTe can be attributed to this internal-strain induced lattice softening effect. While inhomogeneous internal-strain fields are known to introduce phonon scattering centers, this study demonstrates that internal-strain can also soften a materials lattice on average, modifying the speeds of sound and phonon dispersion. This presents new avenues to control lattice thermal conductivity, beyond phonon scattering, with microstructural defects and internal-strain. In practice, many engineering materials will exhibit both softening and scattering effects, as is shown in silicon. This work shines new light on studies of thermal conductivity in fields of energy materials, microelectronics, and nano-scale heat transfer.