Welcome to the LITIengine forum!
So I think there a multiple parts to this question:
Should you use a Spritesheet for 2D Character animation
I'd say yes. It doesn't have to be one giant spritesheet though. The basic principle of the LITIengine is to have one Spritesheet per animation. And the engine provides a simple framework to actually animate this stuff in the game.
"But then how do I change my 1000s of images into a suitable SpriteSheet and is this even viable"
You could a tool like Texture Packer to bunde the images that belong to one animation. And I would highly suggest to separate the spritesheet because otherwise you'll have to deal with a lot of magic numbers.
"I get the feeling what I want to achieve is a lot more complex than what these libraries provide. It also has its own custom .map files."
Of course from the screenshot that you provided, it might not always be obvious which images belong together and I think that this logic is part of the game logic that you're trying to recreate. Guess it's up to you to find out that boundaries.
It also has its own custom .map files.
The LITIengine in its current state only provides support out of the box for
.tmx maps. Now I'd say it depends on the
.map format of the game that you're trying to re-create and whether it's plain text or binary. If it's plain text I think there should be a way to transform it into a more general format.