Can electric field lines do work?

Answer 1

Yes.

Work is force times distance, or technically the dot product of vector force times vector distance. Electric fields exert force on charge and the force does work when the charge moves in the direction of the electric force. (In the converse, when the movement of charge is against the direction of force, work is transformed into stored electromagnetic energy.)

Technically, it is the electric field that does work and not the field line.

Mother nature produces electric fields, but humans can not see electric fields. Humans invented the idea of field lines to create a mental picture of the field. The two most common ways are to draw lines in space or to draw a collection of arrows in space.

Note:

One should not confuse this answer with the question of whether work can be done by a magnetic field. A magnetic field can not do work because the direction of the magnetic force is always perpendicular to the direction of motion of charge and hence the dot product of force and distance moved is always zero.

Answer 2

No, electric field lines themselves do not do work. They simply represent the direction and strength of the electric field. Work is done when a charged particle moves in an electric field, experiencing a force due to the field.