Amazon Lumberyard is the weirdest name for an engine lol
game engine made by amazon
I don't think Unreal/Unity fit the definition of Open Source Software
they are technically free because they give you free license to use
payable is more like you pay and then only have the right to use the engine
You only pay when you develop for consoles or sell your game
You might get access to the source code but there are restrictions on how you can use it.
I can download UE4 right now
There are two definitions of "free": one is you don't have to pay money, the other is on "freedom".
While you can use download Unity/Unreal for free, you are not free to use it and sell your games without paying royalties.
But you are free to release the game for free
Maybe a publisher can notice your project and pick it up to publish it
but again there are private game engines which are not free and are made exclusively for the studios
or engines which require you to buy them before you can start using them