It depends on how IT configured Respondus Lockdown Browser.
Normally, the assignment that is set up for Respondus Lockdown Browser is the only thing the students can access in that window.
It is possible to set up Respondus Lockdown Browser so that the student can do other things in that one browser window, but almost nobody sets it up that way.
The only way to know for sure is to set up a quiz and ask a student to take it. See what they can and can not do, while resetting the Lockdown Browser. Be aware that students are skittish about Respondus Lockdown Browser and will not want to try things that can get them flagged.