If we wanted to play manually, one person with a stuffload of lego (if I were at my aunt's, that could be me) builds the things the players send photos of to them, then manages the game assuming they have a big chunk of table space they can leave crap on for weeks at a time. They then take photos of the game board as it stands, post them, and each player tells them what their moves are (note it on the images, draw arrows etc)
The manager then does those moves, posts an updated board, and you repeat until finished. Would make a short game take days though. A long pitched battle would take weeks.
Alternately, the manager could just have topdown photos of all the player's constructions if they can get them in, and build the gameboard in photoshoop.
