We demonstrate theoretically the feasibility of correlated photon-pair generation with vanishing threshold in a bimodal cavity setup that uses a single V -type three level atom pumped by dual incoherent sources and driven by two coherent fields. The photon-pair is shown to be entangled only for low levels of the incoherent pump and owes its origin solely to the coherent drives. The steady-state features as regards the average photon numbers, intra-and inter-mode Hanbury-Brown-Twiss (HBT) correlation functions are studied in detail. We show that the dual incoherent pumping with no coherent drive can lead to amplification of the cavity fields with strong inter-mode antibunching but no entanglement. We analyse our results in terms of an interplay between coherent and incoherent processes involving cavity-dressed states. Both the interand intra-mode HBT functions exhibit temporal oscillations in the strong-coupling cavity QED regime.Our theoretical scheme for the generation of nonclassical and entangled photon pairs may find interesting applications in quantum metrology and quantum information science.