Can a method of research used in one context be reused in a different research context? Is it permissible to reuse a methodology in another context. e.g.  One did a research on land surface temperature(LST) based on a model, say for it. Now is it legit to follow all the procedures of this research for forest loss modelling? Care that just majority are same (in methodology part) but one uses for LST and another for forest loss.
Yes, it is possible - it happens a lot. Epidemiological methods that originated in health have been applied to other fields, for example.

Doing it is easy.

Doing it rigorously, in keeping with the standards expected in academia, is really hard. It's hard because the source field's methodology usually has a lot of tacit assumptions built in. Identifying those, and testing they're applicable to the application field, is difficult. Lazy researchers don't bother doing that testing, and produce shoddy work as a result.