LAMP consist of Linux, Apache, MySql and PHP whereas LEMP consist of Linux, Nginx, MySql and PHP. With LEMP, Apache is replaced with the lightweight yet powerful Nginx which has its own benefits.
No real reason unless you know what you are doing. People usually opt Nginx for heavy traffic websites or websites which need the best results. Where some comparisons with Apache 2.4 vs Nginx shows Apache 2.4 is not very bad as compared to Nginx. Additionally to manage LEMP, you should know to manage/configure Nginx [ thought its pretty easy, has good docs and pretty decent user base ] . So it is up to you...may be you can start with LAMP....if you do not feel comfortable with its speed and other factors try LEMP.