Abstract: We consider a flavour conserving two Higgs doublet model that consists of a type I (or X) quark sector and a generalized lepton sector where the Yukawa couplings of the charged leptons to the new scalars are not proportional to the lepton masses. The model, previously proposed to solve both muon and electron g – 2 anomalies simultaneously, is also capable to accommodate the ATLAS excess in pp -> S -> tau(+)tau(-) with gluon-gluon fusion production in the invariant mass range [0.2; 0.6] TeV, including all relevant low and high energy constraints. The excess is reproduced taking into account the new contributions from the scalar H, the pseudoscalar A, or both. In particular, detailed numerical analyses favoured the solution with a significant hierarchy among the vevs of the two Higgs doublets, t(beta)similar to 10, and light neutral scalars satisfying m(A) > m(H) with sizable couplings to tau leptons. In this region of the parameter space, the muon g – 2 anomaly receives one and two-loop (Barr Zee) contributions of similar size, while the electron anomaly is explained at two loops. An analogous ATLAS excess in b-associated production and the CMS excess in ditop production are also studied. Further New Physics prospects concerning the anomalous magnetic moment of the tau lepton and the implications of the CDF M-W measurement on the final results are discussed.