I have created a large number of tasks for my team, but the people that the tasks are assigned to are unable to change the assignees. In the picture below you can see that the task is assigned to scott lyons, and that this user is logged in, but the padlock appears next to the list of assignees so they can't be changed. I can get around this by changing the project to "Open" under advanced settings, but I'm surprised that someone that the task is assigned to can't change the assignees in a "Locked" project.
The whole purpose behind a locked task is that a user cannot reassign a task without the owner knowing it. Therefore, the task creator (owner) can change the assignees, but they have to unlock the task first.