Right. Every possible chess game as a sequence of legal positions can be uniquely enumerated. Per Wikipedia the game-tree complexity is around 10^123, so you'll need about a 124 digit number to represent them. This is as dense as it can possibly get.
On the other hand, lichess supports alternative chess modes and starting boards that may or may not be reachable from the standard initial configuration and legal moves, so this won't work for those use cases.
On the other hand, lichess supports alternative chess modes and starting boards that may or may not be reachable from the standard initial configuration and legal moves, so this won't work for those use cases.