"Division lobbies" refer to separate rooms or areas in a parliament or legislative body where members can gather to cast their vote on a particular issue. Full definition
A furious David Cameron was reported to have confronted the leader of the rebellion, Jesse Norman MP, just outside the House of Commons division lobbies late on the night of the vote as it became clear that normally loyal Tory MPs were determined to register their opposition. (telegraph.co.uk)
This group of MPs haven't been prepared to blindly let themselves be ushered into whichever division lobby Cameron and Clegg want them to. (politics.co.uk)
One said: «You know how to vote when you see who's in the other division lobby.» (theguardian.com)