T&S said the introduction of the Instants scratchcard game in March meant its lottery sales would reach pounds 100m in its first full year.
Chief executive Jim McCarthy said: "Those branches with the lottery do outperform those that do not have it. Convenience stores are doing well due to their good locations and long opening hours."
Overall the lottery factor boosted T&S pre-tax profits by 15 per cent to pounds 8.1m in the six months to July.
Sales rose by 15 per cent to pounds 217m, but T&S acknowledged that the success of the lottery had dented sales of other products in some of its smaller Supercigs outlets. Supercigs is now selling discounted magazines through 150 of its 318 outlets and plans to start discounting tabloid newspapers soon. The price of titles such as The Sun and the Daily Mirror will be cut by around 5p.
The number of Dillons convenience stores has increased by 35 to 183 over the year. Likefor-like operating profits increased by 24 per cent. The division is now moving towards a full electronic point of sale system. T&S plans to have more than 200 convenience stores by the end of the year.
The shares were unchanged at 199p.