Sorry, only just seen your reply now.
Difficult to suggest because its not my project so I don't know what might work based on the contents your using
However, one thought that comes to mind for doing that would be with physics applied to your net cache to film it covering the lion.
So maybe that would be my first project for this part of the video. The lion getting covered by the cloth.
I have included a video (at the bottom) of Marks from his SmallWStudio utube chanel that shows the basics of what I mean in case your not sure of that.
By the way. He has a lot of great tutorials that shows ways of creating animated scenes that may help you to watch.
For lifting the captured lion I might make a second project with the lion positioned inside of and linked to a content shaped like the cloth lifting the lion.
That way pulling that content up will also pull the lion up and you shaping the lions body with the lions 'edit motion layer' so it looks caught in the cloth content.
Geez im getting old to explain things LOL
Anyway, I would then use the outputs from those 2 projects (and most likely many other projects) in my video editor, I use hitfilm pro, to put the entire video together
One of the reasons I do things like that as separate projects because its easier to change things when its not all in 1 project without affecting the animations that come after the one I am adjusting.
Creating the lion getting covered/captured by the cloth and then the lion getting lifted as separate projects makes sense to me because your likely to have camera changes between those two parts of the scene anyway. Having them as separate projects also makes it easier to use a set of contents to do the first part of the scene and a different set of contents in the second part of the scene that look similar enough.
As I said, Its difficult to say exactly what to do when its not my project. But these are just some thoughts that might help you do what you intend.
Hope so anyway. Ultimately, you will need to decide how to do it.
SmallWStudio
i7-3770 3.4GHz CPU 16 GB Ram
GeForce GTX1080 TI 11GB
Windows 10 Pro 64bit