No, you cannot directly reopen or reassign a closed lead.

Once the lead has been closed in the Com Portal, it will move to the "Closed" bucket, and the checkbox will now be grayed out and inactive, as shown below. 

While you cannot reopen the closed lead directly, you can start a new communication with that lead to open a new engagement thread. In this case, the original lead engagement will remain closed, but it will be connected to a new email or SMS conversation in the Com Portal.

Learn more about how to "reopen" or reassign a lead here.