Leask replaces Rob Graham, who is on leave from the company due to illness, and will handle Lidl's £12m promotional budget. The firm's current strategy focuses on one-off weekly offers in the national press.
Last year, it tied with Air Berlin to offer £19 one-way flights during a week in September to European cities including Vienna and Zurich.
The German chain is the eighth-biggest retailer in the UK, with 2.2% of the market, according to TNS.
In terms of discount supermarkets, Lidl is second only to Aldi in the UK, with a 2.6% share.