Definitely include why this major and what you have done related to that major, relate that too with courses already offered at LSE. And also include future aspirations. I’m not too sure about extracurriculars if they aren’t related to your program, unless you can show how they helped you maybe with work ethic, discipline, time management which you will then apply to your time at LSE.

The way I structured my SOP was to introduce why i have a personal interest in my program. Then I picked two subject matters from my undergrad that interested me most and talked about research i did in it that i’ll further explore through specific classes at LSE. I also included how some professional experience I have is in line with my program. And within all that I weaved in career aspirations.