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.
Yes, you can use a good design used in other contexts. You will need to cite the article. In practice, you will need to be very careful when writing the methodology section: It will necessarily be very close to the original article. If it gets too close, you'll run the risk of being accused of plagiarism.
Can is the wrong term. Must is the correct one.
Research and science rely on the possibility to replicate and novel methods have always been the engine for new developments and achievements.
If you don't use your own method when it is appropriate to do it, why should other people bother?
Success in research and science often goes to those who have discovered new methods, rather than simply new ideas and theories. For instance, look at The Top 1000 Papers by Van Noorden et al, in Nature 2014. It is clear that the most successful articles are those reporting methods which can be successfully replicated and exploited for further research and applications.