  We present a new release of the RELTRANS model to fit the complex
cross-spectrum of accreting black holes as a function of energy. The model
accounts for continuum lags and reverberation lags self-consistently in order
to consider the widest possible range of X-ray variability timescales. We
introduce a more self-consistent treatment of the reverberation lags,
accounting for how the time variations of the illuminating flux change the
ionisation level of the accretion disc. This process varies the shape of the
reflection spectrum in time causing an additional source of lags besides the
light crossing delay. We also consider electron densities in the accretion disc
up to $10^{20}$ cm$^{-3}$, which are found in most of the stellar mass black
holes and in some AGN. These high densities increase the amplitude of the
reverberation lags below $1$ keV since the reflection flux enhances in the same
energy range. In addition, we investigate the properties of hard lags produced
by variations in the power-law index of the continuum spectrum, which can be
interpreted as due to roughly $3\%$ variability in the corona's optical depth
and temperature. As a test case, we simultaneously fit the lag energy spectra
in a wide range of Fourier frequency for the black hole candidate MAXI
J1820+070 observed with NICER. The best fit shows how the reverberation lags
contribute even at the longer timescales where the hard lags are important.
This proves the importance of modelling these two lags together and
self-consistently in order to constrain the parameters of the system.
