This paper reports a search for a light CP-odd scalar resonance with a mass of 20 GeV to 90 GeV in 13TeV proton-proton collision data with an integrated luminosity of 140 fb(-1) collected with the ATLAS detector at the Large Hadron Collider. The analysis assumes the resonance is produced via gluon-gluon fusion and decays into a tau(+)tau(-) pair which subsequently decays into a fully leptonic mu(+)nu(mu)(nu) over bar (tau)e(-)(nu) over bar (e)nu(tau) or e(+)nu(e)(nu) over bar (tau)mu(-)(nu) over bar (mu)nu(tau) final state. No significant excess of events above the predicted Standard Model background is observed. The results are interpreted within a flavour-aligned two-Higgs-doublet model, and a model-independent cross-section interpretation is also given. Upper limits at 95% confidence level between 3.0 pb and 68 pb are set on the cross-section for producing a CP-odd Higgs boson that decays into a tau(+)tau(-) pair.