TBM allows to assign users to Trados Live tasks. To do that, please follow the steps below:
1. Open Reference data > Service types page. Here, select your services one by one and click RWS > Trados Live > Link with existing task type:

This allows to establish connection between TBM services and LC tasks, so TBM will “know” which tasks you’re going to assign and correctly pickup assignments containing necessary services.
2. Create/open some translation project. It should contain assignments with non-empty Vendor field and filled Tasks table. Preferably, a file should be added to the list of files – this will allow TBM to correctly connect LC task and TBM assignment, by comparing file names. If you don’t add a file, probably TBM won’t be able to determine an assignment automatically, but you will be able to select it manually.
3. Link translation project with Trados Live project (or create Studio Live project from TBM).
4. Click RWS > Trados Live > Manage project assignees:

The following dialog opens:

Here you can view all non-completed tasks from a project, along with file names and languages. In the last two columns (Assignment and New assignees) you can make your selections. If TBM project has an assignment which matches to Trados Live file/task combination, this assignment will be selected automatically, and vendor will be added to the New assignees field. Otherwise, you can make selections manually.
Green row background signals to you that after clicking Apply button that row will be processed. Grey rows will be skipped.
Take a note that list of vendor in the New assignees field will contain only vendors which are linked with Trados Live users. So, please establish these connections in advance.
5. When you’re ready, click Apply button. TBM will send necessary requests to Trados Live server, assigning selected vendors. Language Cloud will automatically send necessary notifications to users. When operation completes, you will see confirmation dialog, like this:

or this:

6. If operation completed successfully, contents of the dialog will be updated, and you should see newly assigned users in the Current assignees column.