How do you fix a flush handle that will not push down? It will not move. The toilet will flush if I remove the lid and pull up on the chain.
I suggested above in the comments section that you should be posting a picture of the inside part of the flush lever for evaluation. That said if the lever does not want to move then there are two good possibilities here, both of which will likely require replacement of the lever assembly with a new generic unit.
The first possibility is that the current non-functioning lever is all made out of metal and has been in the tank for literally ages. Many times the rotation point where the lever assembly passes through the wall of the water tank builds up deposits and/or corrosion to the point that the lever can no longer be moved. Another possibility is that the fastening nut that holds the lever in place has come loose and allowed the collar in the hole to turn. The collar usually has a built on stop that limits how far the lever can be moved. If this collar turns then the limit stop may be what is keeping the lever from turning.
The other possibility, which is much more common on more recent day toilet installations, is that the flush lever assembly is made all or partially out of plastic. These have the advantage is being less susceptible to the corrosion problem but can have problems of their own. These can also have problems with the turning collar issue if there is a bad match between the collar size and the typical square hole through the water tank wall. Plastic assemblies can break which is often caused by the plastic getting old and brittle. Breakage can manifest itself in the rotating part of the lever mount and prevent proper operation.