Use LC API to retrieve and replicate online editor data in home-grown CMS

One of my accounts would like to use LC API to develop integration between Trados Enterprise and their home-grown CMS. Their CMS will have an editing environment and the customer would like to replicate as many online editor features as possible via API to allow their users to perform online editor-like tasks in their CMS, such as translation/review/TM & TB Lookup etc. Once the translation and review tasks are done in the CMS, they would like to update the TM in Trados Enterprise.

Could you kindly advise which API they should use to achieve this objective?