From time to time, AC may have seat sales for Biz Class but no, price would not usually go down closer to departure. In some cases, the Bid Upgrade, if successful, may result in savings vs buying the ticket upright. The other option is a "last-minute upgrade" usually offered during check-in, if seats remain available for such thing (IE: a certain # of seats may still be left open for members of AC's frequent flyer program using eupgrade credits so LMU may not always be offered)