"The main objective of well 16/4-8 S is to test the reservoir properties and verify the petroleum potential," the company said in a statement.
Luno II is situated in the Norwegian waters of the North Sea. Drilling is expected to take about 50 days.
Lundin said last year it estimated Luno II may be able to produce as much as 160 million barrels of oil.
The Swedish energy company, operating through a Norwegian subsidiary, said about 75 percent of its oil production comes from Norway.
Last week, the Norwegian Petroleum Directorate said 1.66 million barrels of oil were produced in the country in May on average. That's 13 percent lower year-on-year, but 5 percent above what it had expected for the month.