Chapter 11 of the book describes a model for the QBO of stratospheric equatorial winds. The stratified layers of the atmosphere reveal different dependencies on the external forcing depending on the altitude, see Fig 1.
Well above these layers are the mesosphere, thermosphere, and ionosphere. These are studied mainly in terms of space physics instead of climate but they do show tidal interactions with behaviors such as the equatorial electrojet .
The behaviors known as stratospheric sudden warmings (SSW) are perhaps a link between the lower atmospheric behaviors of equatorial QBO and/or polar vortex and the much higher atmospheric behavior comprising the electrojet. Papers such as [1,2] indicate that lunar tidal effects are showing up in the SSW and that is enhancing characteristics of the electrojet. See Fig 2.
“Wavelet spectra of foEs during two SSW events exhibit noticeable enhanced 14.5‐day modulation, which resembles the lunar semimonthly period. In addition, simultaneous wind measurements by meteor radar also show enhancement of 14.5‐day periodic oscillation after SSW onset.”Tang et al 
So the SSW plays an important role in ionospheric variations, and the lunar tidal effects emerge as the higher atmospheric density of a SSW upwelling becomes more sensitive to lunar tidal forcing. That may be related to how the QBO also shows a dependence on lunar tidal forcing due to its higher density.
- Siddiqui, T. A. Relationship between lunar tidal enhancements in the equatorial electrojet and stratospheric wind anomalies during stratospheric sudden warmings. (2020). Originally presented at AGU 2018 Fall Meeting
- Tang, Q., Zhou, C., Liu, Y. & Chen, G. Response of Sporadic E Layer to Sudden Stratospheric Warming Events Observed at Low and Middle Latitude. Journal of Geophysical Research: Space Physics e2019JA027283 (2020).