Lolth's Immanence

Leg of the Goddess
Immediately following the first fight with Lolth's Immanence, Lolth will attack the party with her eight legs. Upon destruction, each of the legs will turn into a Bebilith Soul. You can see where the leg is about to pop up if you look at the ground. The party should focus on one leg at a time, because if the leg doesn't die and goes back into the ground it fully heals itself. The safest strategy is to go Leg then Bebilith until all the legs are down. Once all the legs are destroyed, Lolth's Immanence will return for a second fight.

Hand of the Goddess
Following the second fight with Lolth, her hand will appear. The hand is invulnerable (it can be damaged, but instantly regenerates if damaged much), but can be pulled away from the party with a successful intimidate check. If you lack intimidate, you can damage it via any untyped/force spell damage such as Blade Barrier. If you lack both spell casting and intimidate, you can use certain destiny abilities such as Orchid Blossom from Grandmaster of Flowers or Wild Shots from Shiradi Champion.

As of Update 15, the hand sticks around for a much shorter period of time. It no longer needs to be kited until the end of the raid.