Presiding over gatherings in the secretary’s office was just one way Mr. Lewandowski exerted power far beyond the scope of his role as unpaid adviser. While he joined the department early last year in what was supposed to be a limited, part-time role, the longtime Republican operative used his perch to build an expansive portfolio in which he had wide influence over personnel, contracts and the department’s operations on the ground, according to nearly 20 current and former administration officials, many of whom spoke on the condition of anonymity out of fear of retaliation.