Can the lag phase time be reduced? Yes. You can truck in sludge from a compatible plant with the same waste or in many cases it is easier to inoculate with a bioaugmentation product suited to the waste/system. By adding adapted cultures to the existing microbes, the adjustment time can be significantly reduced which can reduce holding back influent, adding extra polymers/antifoams, or having effluent permit issues.
Can you predict if adjustment will be an issue? Once again yes. You can do bench testing with oxygen uptake rates and various toxicity testing to determine if the new waste will be an issue. I have discussed both heterotrophic and nitrifier toxicity testing in previous posts.