The family of rare-earth (R) tritellurides RTe3 features charge-density-wave (CDW) order related to strongly momentum-dependent electron-phonon coupling. Similar to other CDW compounds, superconductivity is observed when the CDW order is suppressed via hydrostatic pressure [J. J. Hamlin, Phys. Rev. Lett. 102, 177002 (2009)10.1103/PhysRevLett.102.177002]. What sets the heavier members of the RTe3 series apart is the observation of a second CDW transition at lower temperatures having an in-plane ordering wave vector qCDW,2 [100] of almost the same magnitude but orthogonal to the ordering wave vector qCDW,1 [001] observed at higher temperatures [N. Ru, Phys. Rev. B 77, 035114 (2008)10.1103/PhysRevB.77.035114]. Here, we report an inelastic x-ray scattering investigation of the lattice dynamics of DyTe3 In particular, we show that there are several phonon modes along both in-plane directions, which respond to the onset of the CDW transition at TCDW,1=308K. Surprisingly, these soft modes close to qCDW,2=(0.68,0,0) show strong softening near TCDW,1 but do not exhibit any response to the lower-temperature transition at TCDW,2=68K. Our results indicate that the low-temperature CDW order is not just the 90° rotated analogue of the one appearing at high temperatures.