Vectors that facilitate the engineering of T cells that can better harness endogenous immunity and overcome suppressive barriers in the tumour microenvironment would help improve the safety and efficacy of T-cell therapies for more patients. Here we report the design, production and applicability of T-cell engineering of a lentiviral vector leveraging an antisense configuration and comprising a promoter driving the constitutive expression of a tumour-directed receptor and a second promoter enabling the efficient activation-inducible expression of a genetic payload. The vector allows for the delivery of a variety of genes to human T cells, as we show for interleukin-2 and a microRNA-based short hairpin RNA for the knockdown of the gene coding for haematopoietic progenitor kinase 1, a negative regulator of T-cell-receptor signalling. We also show that a gene encoded under an activation-inducible promoter is specifically expressed by tumour-redirected T cells on encountering a target antigen in the tumour microenvironment. The single two-gene-encoding vector can be produced at high titres under an optimized protocol adaptable to good manufacturing practices.