Has he had his interview yet? My child’s interviewer seemed to be looking for specific and solid reasons for why they wanted to attend Lakeside. Your son will want to communicate clear and well defined reasons as to why Lakeside will provide a better education/learning environment than his current private school.
He should also communicate what he will contribute to Lakeside–preferably something that Lakeside is currently missing. I think Lakeside is looking for as diverse of a student body as possible. If he is an URM, first generation college, obtained state-level in any activity, or possess a unique skill or have had a unique experience–your son needs to stress this in both the interview and the application.
While his SSAT score is phenomenal, his GPA will hurt him. I think if he is a superstar in something, or can offer something unique to Lakeside, he may be able to overcome his GPA.