The focus mechanism will be driven by a micro stepper motor, the driver IC for this is a LB1935FA - a bipolar stepper driver, this requires two logic lines to set the stepping logic 00, 01, 11, 10, etc. or the reverse sequence for reverse, and one for enabling the system (this keeps the current off when not required).

As can be see (upper left, below the connector) the driver is very small, so could be useful for all manner of different projects.

The motor i'm using is 8mm x 8mm diameter, so quite large compared to many available on eBay.

I've found that a 1us coil activation time to be optimal, this gives a nice smooth response. Higher delays seem to be more jarring / noisy.