Note: I am sharing this method. There is also a method to Lock accounts in just 2 hours.
How To Perm Lock Someones Xbox Live Account- ( this isn't my main method also I am the one who created this method.)
(3-5 day process) ( Works 80% of the time. )
Step 1: First call up xbox billing department ( 800-469-9269 ) wait for the recording to be done and dial (1) then keep dialing (0) until it gets you to a agent. Once you get to a agent say that you want to update your account info and that you called earlier and updated your info and wanted to make sure they put the right info. They well ask your for a reference number and say that you threw it away. They will say ok sir. They will ask for the tag and give them the tag you want locked. When they ask for name,address and the info give them fake info but, REMEMBER the info for later. While verifying the info say " What the fuck my gamertag just signed on to another console but, I only have one console I think someone just hacked my gamertag" They well say ok sir. Ask them for a reference number make sure you get that reference number. Say you well call back later and finish this but you need a reference number so they can pull up the tag instantly. One you get that reference number go to step 2.
Step 2: Call up xbox billing department ( 800-469-9269 ) again wait for the recording to be done and dial (1) then keep dialing (0) until it gets you to a agent. (make sure it's not the same agent. Once you get to a agent give them the tag and tell them your have a reference number on your problem. Once they pull up the gamer tag and ask you what the problem is tell them not just long ago someone took your gamertag while you were on the phone with xbox. They well then ask you to verify the info give them the same fake info. They will say its incorrect say " O my god I think they changed my info too but, they will say their wasn't any recent changes on it. Tell them you like to open a AU on the account. WHen they ask for console ID and serial tell them the back of your console is scratched and you can not read it. Say this " ok let me turn on my console and get it for you ". They will say ok. Then say " what the hell I just got the red ring of death theirs no way I can get my console id now." They will say ok. Say can you please still open a AU on the account and send it in so the investigation team can still take a look at it. They will say ok. Ask for a reference number. Then hang up and repeat the whole guide again.
After you've done this 2-3 times the account will be perm locked within 3-5 days.
Seems like a lot of work, when you can just block communications. Plus, the actual owner of the account could just call up Microsoft themselves and get their account unlocked.