Izalith Shortcut in NG+?

I got to Chaos Follower +2 during this playthrough, because I absolutely hate the lack of effort that the Izalith lava section represents.

Since I considered going to SL150, I was planning to leave the Followers and go all Sunbro on this character. But what will happen to the shortcut? Should I go to NG+, open it and then join the Sunbros? Or will it be already be open for me as soon as I hit NG+?

You'll have to open it before joining Sunbros Covenant or the shortcut won't be available.

See MotoPsycho's answer below., thanks Moto I did not know that

Open it, then do what ever, It stays open. (physically open it before leaving the covenant though)
And you have to re-open it on every NG+.

Great, thanks!

Also: you can open it from the other side, no Daughter of Chaos covenant allegiance required whatsoever. You just need to go the long way around once, then you can go rest at the bonfire behind Firesage and never go to the lava again. (This is especially useful when you want to invade, since invading just past the shortcut door, on the Izalith side, is a relatively short walk from the bonfire, and you spawn in front of BoC's door, rather than in the lava.)