Does anyone know what the chances of an offer are if placed on the reserve list for LSE (LLM)?

I don't think anybody here could give you an accurate answer, since there are so many variables, including the profiles of the admitted candidates, your profile, the number of applications received, and more. This all varies year-to-year, but you can browse through past threads on the reserve list, for example:

https://llm-guide.com/board/uk-ireland/lse-reserve-list-82866

... to see what happened to other reserved candidates.