A lance injector for a gas turbine engine, the lance injector comprising: a supply duct arrangement, including at least a first tubular body and a second tubular body, concentrically extending along a central axis; and a terminal member coupled to downstream end of the supply duct arrangement; wherein a fuel oil supply duct is defined inside the first tubular body and a shielding air duct is delimited by the first tubular body internally and by the second tubular body externally; wherein the terminal member has a central fuel oil nozzle, coupled to the fuel oil supply duct, and an air outlet, coupled to the shielding air duct and surrounding the fuel oil nozzle; wherein the fuel oil nozzle is configured to deliver a fuel oil flow in a hollow cone pattern; and wherein the air outlet is configured to direct a shielding air flow from the shielding air duct such that the shielding air flow crosses the delivered fuel oil flow, wherein a direction of an airflow velocity at the air outlet intersects the delivered fuel oil flow and intersects the central axis; characterized in that the terminal member comprises a hollow first convergent body, connected to the first tubular body and forming a fuel delivery chamber fluidly coupled to the fuel oil supply duct and to the fuel oil nozzle and wherein the fuel oil nozzle is formed in the first convergent body of the terminal member; wherein the terminal member comprises a hollow second convergent body, connected to the second tubular body, and wherein the shielding air duct has a convergent section delimited by the first convergent body internally and by the second convergent body externally; and wherein the air outlet has an annular convergent shape. a supply duct arrangement, including at least a first tubular body and a second tubular body, concentrically extending along a central axis; and a terminal member coupled to downstream end of the supply duct arrangement; wherein a fuel oil supply duct is defined inside the first tubular body and a shielding air duct is delimited by the first tubular body internally and by the second tubular body externally; wherein the terminal member has a central fuel oil nozzle, coupled to the fuel oil supply duct, and an air outlet, coupled to the shielding air duct and surrounding the fuel oil nozzle; wherein the fuel oil nozzle is configured to deliver a fuel oil flow in a hollow cone pattern; and wherein the air outlet is configured to direct a shielding air flow from the shielding air duct such that the shielding air flow crosses the delivered fuel oil flow, wherein a direction of an airflow velocity at the air outlet intersects the delivered fuel oil flow and intersects the central axis; characterized in that the terminal member comprises a hollow first convergent body, connected to the first tubular body and forming a fuel delivery chamber fluidly coupled to the fuel oil supply duct and to the fuel oil nozzle and wherein the fuel oil nozzle is formed in the first convergent body of the terminal member; wherein the terminal member comprises a hollow second convergent body, connected to the second tubular body, and wherein the shielding air duct has a convergent section delimited by the first convergent body internally and by the second convergent body externally; and wherein the air outlet has an annular convergent shape.