In 3Shape LMS there is no way to completely remove a client profile, only make inactive. This article shows you how to make a client inactive.
1) Client > Client Profiles > Client List
2) Select name in blue
3) Click "Edit"
4) Change Status to "Inactive" and click "Update"
The client is now set as Inactive.
Note: You can always look up your inactive clients by adjusting the filters on the Client List.