I'd like to be able to lock my tree so that it CANNOT be changed. Is that at all possible?
No, not currently in the shared Family Tree - but yes, in Genealogies. There you can submit your static/unchangeable family tree (at least a few generations).
Your request is like asking for Chinese food in a Mexican restaurant.
The whole point of the Family Tree on FamilySearch is that it is collaborative and open-edit. If that is not what you want, then FamilySearch is not where you should be. There are several individual-tree websites available, and there are also many, many genealogy programs or apps that you can use on your computer or other device.
Always keep your own family tree in a place where only you can edit it. Paper or digital, its up to you. I see collaborative trees as only a place to discover information and get ideas. They are certainly not authoritative nor to be considered as sources in and of themselves. I have seen far too many "sources" on the FS sources tab that actually were Ancestry family trees. Talk about circular arguments!!
There's a help center article on this subject:
I've been reading other posts on this matter. Thanks for the comments.
I always do. I even have hard copies. :)