Why was Dawn's (the spacecraft) flight path circular?
Dawn was not exploring L3. But instead it explored both Vesta and Ceres. In order to do so in a cost-saving manner, Dawn was also a mission demonstrator for an interplanetary mission equipped with ion propulsion.

Because of the low specific impulse of ion propulsion, Dawn cannot fly in a straight line, as this would imply a high initial velocity and the spacecraft couldn't deaccelerate in time. Therefore, Dawn started with low $v_0$ at Earth, and raised its orbit slowly and continuously, creating the spiral you see.