The bus services are also run by TfL (who also manage the A23) and not by Lambeth. Bus priority on Streatham High Road has increased - the bus lanes changed to At All Times (from m-f peak hours) in 2020/21. There probably is scope for extending bus lanes further and using traffic light 'gates' to give buses priority where it's too narrow for bus and general traffic lanes.
Public transport services require subsidy and TfL's funding is effectively set by central government. COVID destroyed TfL's reserves and they have had to fight for every grant and to maintain existing bus services (which run at a loss).
New funding from the Mayor saves vast majority of London's buse
tfl.gov.uk
In any case, I don't think better bus services would do anything to appease the majority of complainants about Streatham's LTNs