Question about Bahamut's Coil Lockout

So I have been searching all over the forums and the internet in general for a definitive answer for this so I am hoping someone here would know...

I understand that Bahamut's Coil has a weekly lockout and how even if you didn't do turn 1 or 2 but you help on turn 3 or 4 you are locked out of all the turns up to the turn you actually did complete.

My question is this... I have two characters on my one acct. Both of them are level 50 and have all the pre-reqs done individually to complete Bahamut's Coil. One of them is a healer and the other is a dps. I like to keep my healing and dps characters seperate even though I can level each class up to 50 on one person. Is it possible to help my FC out on Coil raids as a healer and as my dps since it is with 2 different characters on the same account or is the lockout acct wide? I am really unsure since there is a lot of conflicting info out there.

Thanks in advance for the help!

Lockouts are character-specific.

Thank you so much for the quick response! Now I feel less like a goof for making two seperate toons to help out my smaller FC.