Lockheed Martin Corp. is barred from selling perhaps its most important product—the F-35 Joint Strike Fighter—in much of the Middle East, but that hasn’t stopped Chief Executive Marillyn Hewson from visiting the region three times in her first year at the helm of the world’s largest defense contractor by sales.

The trips are part of Ms. Hewson’s efforts to tackle one of her top challenges: expanding Lockheed’s international business at a time when its biggest customer, the U.S. government, is slashing spending. She is trying to shift the company’s Washington-focused sales culture, and expand into regions where Lockheed has had a more limited presence.

U.S. export restrictions bar all but two key allies in the Middle East—Israel and Turkey—from acquiring the advanced, radar-evading F-35, at least for the next few years. The limits reflect one of the difficulties of building Lockheed’s future growth on foreign customers. […]