What are 'LMU' and certificates?

LMU is simply Last Minute Upgrade. These upgrades can happen for a variety of reasons. Airlines sometimes offer free upgrades to highly ranked elite level flyers if there are empty seats. Airlines may sell empty first class seats at a discount at the gate if there are lots of empty seats. Travelers can sometimes use frequent flyer points or certificates to upgrade themselves at check in (though folks who use this last method tend to do it further in advance to assure themselves of seats rather than waiting until the last minute).

Certificates are simply a coupon that you can exchange for upgrading one class (ie economy to business, business to first class). Certificates come in a wide variety of forms, some for one flight only, some for all flights in that leg, some for round trip. Certificates can be "bought" with frequent flyer miles, awarded to elite level frequent flyers, given away as compensation for being bumped, delayed or other issues. Some corporations buy certificates to give away to employees, customer, etc