is it possible to change the order of the menu in the Quick Launch in treeview mode only ?
According to your post, my understanding is that you want to reorder the
Tree View of the site contents in SharePoint 2013.
Per my knowledge, we only can
enable or disable the Tree View in the
Site Settings, there is no out of box way to reorder the Tree View in SharePoint as DareDevil say.
As a workaround, if you simply want to hide some lists which is not necessary from the Tree View, I recommend that you can select the Hide from browser check box in the General Settings of these lists by using SharePoint Designer 2013.
Also, you can try to add some proper prefix on the names of the site contents to regularly reorder the Tree View based on your need.
And, if you still want to implement the customizable order of the Tree View, you need to customize own code to create a new Tree View to get the site contents dynamically and add it into the master page to replace the default Tree View.
There are some articles as below for your reference: