lag != local framerate problem != ping.
Whatever, the discussion is going OT, and the map is already gone, as far as I can see.
Like I said, if a single map is "laggy", it is not network lag, but framerate problems. Map size or complexity has nothing to do with network lag, if the same amount of players are present as in other maps.
But now that I think about it, map complexity might slow the server down a little, because if there are lots of objects, the collision datastructure is bigger, making collision checks a bit longer. However, i do hope they use some space partitioning datastructure for collisions, which would greatly reduce the effort, actually making map complexity a non-issue in this regard.
Still, moving the same server hardware to the local area network wouldn't help at all.
Also, if you have bad ping, you will always notice network lag and if you got network lag, you almost always have bad ping as well. Bandwidth doesn't matter much in games networking. The only possibility where you have good pings and still lag is when there are traffic shaping rules in effect that don't delay the ping packets but do delay the other packets of the game's network communication. This should be quite rare, though.
Still, moving the same server hardware to the local area network wouldn't help at all.