for most of the situations its a simple matter of doing some checks such as seeing if the enemy is in range of the player and the proper action has been called (throw, lift, attack).
from there you play a animation. for the throw and lift you would play a grab animation and at a specific point in the animation attach the player to the ai’s hands (socket), oh and disable the players input here if needed. for the pounce you play a hop attack anim.
the last step would be to execute the script for the specific action. for the throw you detach the player from the ai actor and apply a force which sends them flying (look into physics interactions / launch character for this). for the lift your already done unless you want to add in a way to put down the player or have them break free. for the pounce you would just need to add in a attack script and apply damage which will vary depending on your implementation (melee, fps, can attack miss, etc).