With the appearance of the COVID-19 pandemic, the practice of e-learning in the cloud makes it possible to: avoid the problem of overloading the institutions infrastructure resources, manage a large number of learners and improve collaboration and synchronous learning. In this paper, we propose a new e-leaning process management approach in cloud named CLP-in-Cloud (for Collaborative Learning Process in Cloud). CLP-in-Cloud is composed of two steps: i) design general, configurable and multi-tenant e-Learning Process as a Service (LPaaS) that meets different needs of institutions. ii) to fulfill the user needs, developpe a functional and non-functional awareness LPaaS discovery module. For functional needs, we adopt the algorithm A* and for non-functional needs we adopt a linear programming algorithm. Our developed system allows learners to discover and search their preferred configurable learning process in a multi-tenancy Cloud architecture. In order to help to discover interesting process, we come up with a recommendation module. Experimentations proved that our system is effective in reducing the execution time and in finding appropriate results for the user request.