The word lens is just the transparent bit that does the optical focusing.
It looks to me like this is some sort of read / write head from a CD or other optical reader.
Normally with no power these will be in the center.
There are galvanometer coils that do the movement and you have to apply power to these.
I would try what lefty suggested and put out a PWM signal through a transistor or FET to increase the current. However the coils might respond to these rapid signal changes, see:-
http://www.thebox.myzen.co.uk/Tutorial/PWM.html
It could be they need smoothing.
How fast do you want to change the voltage going to those coils?
What sort of resolution do you want with the movement.