What are you applying to study? If Economics, then imo it would be good prep- IF you got an offer, most of your peers will have done econ (even though it is not required).
Be careful what you put forward as your APs (completed and planned, and yes, you have to list them all): LSE can (and could) choose any combination of your achieved or predicted scores to be your offer. Don’t add Econ if it will jeopardize the others.