  Lithium niobate on insulator (LNOI) has a great potential for photonic
integrated circuits, providing substantial versatility in design of various
integrated components. To properly use these components in the implementation
of different quantum protocols, photons with different properties are required.
In this paper, we theoretically demonstrate a flexible source of correlated
photons built on the LNOI waveguide of a special geometry. This source is based
on the parametric down-conversion (PDC) process, in which the signal and idler
photons are generated at the telecom wavelength and have different spatial
profiles and polarizations, but the same group velocities. Such features
facilitate electro-optical manipulations with photons and, at the same time, do
not require an additional compensation for the time delay. We show how the
spectral properties of the generated photons and the number of their frequency
modes can be controlled depending on the pump characteristics and the waveguide
length. Finally, we discuss a special regime, in which narrowband light with
strong frequency correlations is generated at the telecom wavelength.
