The German supermarket attracted a wave of criticism for erasing the Christian symbol from an image of an iconic Greek Orthodox Church used in its own-label Greek range.
The firm told Premier on Wednesday: "We are sincerely sorry for any offence caused by the artwork on our Eridanous product range and can confirm that we will be revising the packaging design as soon as possible."
Dozens of shoppers contacted Premier - and Lidl UK directly - to express their anger at the decision to include the doctored image of an iconic Greek Orthodox church on the Greek island of Santorini.
Lidl, which operates more than 600 stores in the UK, claimed it had never intended to express an ideological or political standpoint with its products or product design.
The picture appeared on Eridanous products available in the UK and in stories across Europe, including moussaka, halloumi and olive oil.
The company continued: "It is clear that an error was made during the latest redesign of the artwork and we are addressing this as a priority."
On Tuesday, the UK's most senior Greek Orthodox Church figure demanded that Lidl apologise and restore the image of the church to its original state.
Archbishop Gregorios, Archbishop of Thyateira and Great Britain, raised concerns the marketing decision had offended believers and Greeks alike.
He told Premier: "It is immoral in my eyes to remove something which is there for 2,000 year and is the symbol that Christ died on the cross for you, for me, for millions of people."
Eirdanous has been on sale in Lidl stores across Europe for more than ten years and marketing designs have undergone a number of changes.