The Lane Departure Warning system does not keep your vehicle centered in your lane, it provides a warning when the vehicle gets close to lane markings and provides small amounts of steering correction to keep the vehicle in the lane. If you are not controlling the steering the vehicle will weave back and forth 4 feet in the lane.
Toyota’s Lane Departure Warning system is not intended to be operated without the driver controlling the steering;
“If the system detects that the steering wheel has not been
operated for a fixed amount of time or the steering wheel is not
being firmly gripped, a warning is displayed on the multi-information
display and the warning buzzer sounds.”