Respondus LockDown Browser will complain (i.e., not launch) if ARDAgent is running, which can be a problem for lab computers. Fortunately, there is a way around this.
Unfortunately, its implemented in a security-by-obscurity way instead of an actual secure way, so I can't really explain all the steps here (obscurity is all we have—there's no real way to lock it down, the way Respondus has it set up).
All I can say is that if you have an account and want to make it so lab computers can still have Apple Remote Desktop enabled and run Respondus LockDown Browser, you should contact Respondus directly, and they'll give you instructions on how to do it. You'll need your admin login to set it up.