I want to know about local climate zone classification and how it can be used in for urban land surface temperature estimation in google earth engine.
Are you then planning to bring your GEE output into an Esri product?
While I do believe you'll find other GEE users here, you're much more likely to get results by posing a question like this over at GIS Stack Exchange, where over 3k GEE-specific questions have been asked, and very many of which have been answered.