Honda Sense lane keeping is only for > 40mph. In addition, you need to press a button if the vehicle completely stops.
Subaru Eyesight goes down to zero and handles stop and go with lane centering. Though I guess provided you've started the adaptive cruise control system above the minimum speed.
It's not smooth though. Once traffic starts again, Eyesight accelerates hard and then brakes hard when it get up to the car, because it's using cruise control and trying get up to speed and there is a minimum speed (25mph? maybe 10mph? i forget) to set the cruise control.
You could try setting the acceleration curve (eco/gentle) and increase the follow distance.
Not sure if it’s different now, but older models activated Lane Keeping Assist at 45mph and keeps lanes down to 40, and always seems to be just out of reach of usefulness in the city, perhaps by design.
LKA is just that, an assist, because if you let it drive it’ll bounce back and forth between the lane markers, not keep you seemingly centered.