  Misfit layer compounds, heterostructures composed by a regular alternating
stacking of rocksalt monochalcogenides bilayers and few-layer transition metal
dichalchogenides, are an emergent platform to investigate highly doped
transition metal dichalcogenides. Among them, (LaSe)$_{1.14}$(NbSe$_2$)$_2$
displays Ising superconductivity, while the presence of a charge density wave
(CDW) in the material is still under debate. Here, by using polarized Raman
spectroscopy and first-principles calculations, we show that NbSe$_2$ undergoes
a doping-driven collapse of the CDW ordering within the misfit, and no
signature of the CDW is detected down to 8~K. We provide a complete
experimental and theoretical description of the lattice dynamics of this misfit
compound. We show that the vibrational properties are obtained from those of
the two subunits, namely the LaSe unit and the NbSe$_2$ bilayer, in the
presence of a suitable field-effect doping, and then highlight the 2D nature of
the lattice dynamics of NbSe$_2$ within the (LaSe)$_{1.14}$(NbSe$_2$)$_2$ 3D
structure.
