Nothing is planned for the other side of the road as far as I know.
It is part of the CRISP process for the 167 LCN+ route, so all stakeholders were notified and given the chance to give their opinions during that process. That doesn't include members of the public but does include community groups. I can't remember if the Richmond Cycling Campaign were involved in this particular CRISP or not, I certainly wasn't.
When I saw the plans, I voiced similar concerns to the principal engineer. They were going to remove the cycle lane on the road as well, but decided not to in the end.
The money comes from TfL and LBRuT has to spend it on 'improving' LCN+ routes like this one.
Jonathan