furnace not staying on for heater!
The flashing lights will likely tell you what's wrong.  Grab the owners manual, and locate the troubleshooting section.  It should have a section describing the meaning of the blinking lights. If you don't have the owners manual, you might be able to find it online, but you'll have to locate the model number first.  Inside the unit there should be a nameplate that lists a bunch of numbers, and other information.  The model number is likely on that, probably right after the words Model Number:, or Model #:, or maybe simply Model:. If you can't find the model number, the user guide, or you just don't know anything about furnaces. You could always contact Lennox customer support, or the company that installed the unit.  



I'm guessing it's a high efficiency unit (which can be verified by looking for PVC piping leading away from the unit toward the outside of the building). If I'm correct, the sounds you're hearing are likely...


"it started blowing cold air" - Inducer fan on.
"then it makes a click noise like something else was supposed to start blowing" - Pilot or main gas valve open.
"but than it made another click and continued for a few minutes" - Spark ignitor trying to light gas.
"than it just goes off" - Pilot fails to prove.
"the red and green lights ... blink one after another" - Unit failed to ignite, system lock out (possibly flashing specific error code).


Without the model number, it's very difficult to provide further assistance.  Watch the flashing lights, and try to notice a pattern. For example, the red light might flash quickly 4 times, then pause. This pattern often tells you exactly what the problem is.