  Motivated by results recently reported by the CMS Collaboration about an
excess in the di-photon spectrum at about 96 GeV, especially when combined with
another long-standing anomaly at the same value in the $b\bar b$ invariant mass
spectrum in four-jet events collected at LEP, we show that a possible
explanation to both phenomena can be found at 1$\sigma$ level in a generic
2-Higgs Doublet Model (2HDM) of Type-III in presence of a specific Yukawa
texture, wherein Lepton Flavour Violating (LFV) (neutral) currents are induced
at tree level. Bounds from Higgs data play a major role in limiting the
parameter space of this scenario, yet we find solutions with $m_H = 125$ GeV
and $m_h = 96$ GeV consistent with current theoretical and experimental bounds.
