  Aims: The aim of the present study is to explore how to disentangle
energy-dependent time delays due to a possible Lorentz invariance violation
(LIV) at Planck scale from intrinsic delays expected in standard blazar flares.
  Methods: We first characterise intrinsic time delays in BL Lacs and Flat
Spectrum Radio Quasars in standard one-zone time-dependent synchrotron
self-Compton or external Compton models, during flares produced by particle
acceleration and cooling processes. We simulate families of flares with both
intrinsic and external LIV-induced energy-dependent delays. Discrimination
between intrinsic and LIV delays is then investigated in two different ways. A
technique based on Euclidean distance calculation between delays obtained in
the synchrotron and in the inverse-Compton spectral bumps is used to assess
their degree of correlation. A complementary study is performed using spectral
hardness versus intensity diagrams in both energy ranges.
  Results: We show that the presence of non-negligible LIV effects, which
essentially act only at very high energies (VHE), can drastically reduce the
strong correlation expected between the X-ray and the VHE gamma-ray emission in
leptonic scenarios. The LIV phenomenon can then be hinted at measuring the
Euclidean distance $d_{E}$ from simultaneous X-ray and gamma-ray flare
monitoring. Large values of minimal distance $d_{E,min}$ would directly
indicate the influence of non-intrinsic time delays possibly due to LIV in SSC
flares. LIV effects can also significantly modify the VHE hysteresis patterns
in hardness-intensity diagrams and even change their direction of rotation as
compared to the X-ray behaviour. Both observables could be used to discriminate
between LIV and intrinsic delays, provided high quality flare observations are
available.
