Like-for-like sales in the first quarter of the year rose 0.3%, after a 0.9% uptick in the previous period. It is the first time in more than five years that Tesco has reported two back-to-back quarters of UK sales growth.
Tesco also said it will sell its Harris + Hoole coffee chain to Caffe Nero in the latest of a series of disposals as the grocer focuses on its core supermarket business.
Lewis said: "We have delivered a second quarter of positive like-for-like sales growth across all parts of the group in what remains a challenging market with sustained deflation.
"In both the UK and internationally, we are putting customers at the centre of everything we do and re-configuring our business to serve them a little better every day. Our new fresh food brands are performing very well, with over two-thirds of our customers having bought products from the new range."
Across the group, like-for-like sales also grew for the second quarter in a row, coming in at 0.9%.
Over the past two weeks, Lewis has also offloaded a number of other non-core assets.
Tesco sold the Giraffe restaurant chain to Harry Ramsden owner Ranjit Boparan, and also disposed of its Turkish operations. And it sold Dobbies Garden Centres for £217m to investors led by Midlothian Capital Partners and Hattington Capital.
Lewis added: "We are encouraged by the progress we are making. By growing volumes, transforming the way we work together with our suppliers, and further optimising our store operating model we are rebuilding profitability in a sustainable way.
"I am confident that the improvements we are making for customers are working and will create long-term value for our shareholders."
The supermarket said that, by its own measure, customer satisfaction has improved by 2% since the start of the year.
It added that the launch of seven new fresh food brands in March has helped meet customers' needs and removed "any reasons for them to shop elsewhere".
Tesco said that shoppers are able to save nearly £1.60 off the cost of a typical basket of 10 of the most popular meat, fruit and vegetable lines as a result.
The traditional big four supermarkets - Tesco, Asda, Sainsbury's and Morrisons - are engaged in a brutal price war that has eroded profit margins as German upstarts Aldi and Lidl continue to take market share. The launch of Amazon Fresh into the UK market is also expected to shake the sector up further.
John Ibbotson, of Retail Vision, said: "The challenge for Tesco is to keep up the momentum. Amazon Fresh won't help but Tesco's vast size is an advantage, as it allows it to keep down prices for longer than its rivals. In the current war of attrition, this could prove decisive.
"Tesco's rate of growth is paltry compared to yesteryear and the future promises low profits and slow sales growth. But given the huge challenges Tesco is facing, this performance by Dave Lewis has to be applauded."