Production from Libya’s largest oilfield, Sharara, was up last month, and Italy’s Eni is hoping to reverse its downturn in production last year. But caution is still the watchword for the country’s oil investors.

Libya continues to enjoy its highest crude production since the third quarter of 2014 with output of around 700,000 b/d. But state-owned National Oil Corporation (NOC) is yet to persuade some of its major international partners that its bullish oil and gas...