LAMP is not the "cloud". It's a stack of an operative system (Linux), web server (Apache), database engine (MySQL) and scripting language (PHP). It's used for hosting web applications.
The vague "cloud" term, ultimately boils down to an internet connected server running Linux or Windows, with various layers of connectivity, applications, API's and storage access on top.
Meaning, if your company uses Microsoft software (which the majority does), a transition to the "cloud" will just mean that parts or all of your Microsoft systems, now are hosted by Microsoft themselves or a third-party, compared to being placed locally.