I have OA in my left knee on the lateral side, will a lateral OA brace slow down the progression of OA if worn all the time?

I do not. recommend this. It will lead to disuse atrophy. Bracing for severe symptomatic knee arthritis especially when there is deformity, or significant arthritic changes in a specific compartment is a good component of conservative management. But at your age, this is not recommended as an all the time treatment. There is very low chance that you have significant knee OA at this age. So focus on PT.