Libya is set for its highest monthly crude output in almost three years due to continued gains from producing fields in the southwest and repairs to power facilities that were briefly offline at the Mesla and Sarir fields in the northeast. But a dispute with German producer Wintershall rumbles on.

As of 25 May, Libya’s average crude production for the month was about 770,000 b/d, surpassing every monthly average since October 2014 when output averaged 860,000 b/d. It is also a hike of...