Calculate or reduce Button press Delay aka Input lag
Would be pretty sure that its not a monitor response problem, its a ping or you pressed it too late problem.
Even if you pressed the ult button, you are not actually ulting until the server receives the signal that you pressed the R key; if in the eye of the server you died before you ulted, you died. The server is absolute.
Ping is calculated in the time it takes for a packet (a small amount of data) takes to go to the server and then come back (in milliseconds). So if your ping is 200 (a pretty bad ping yes) it would take about 0.1s (3 frames) between you pressing R and actually being in ult in the eye of the server.
There's a checkbox in the options to show your current ping, I just don't remember what is the name.
But your ping is only 50, so I would guess that you should just try to take a habit to activate a little earlier. In LoL you can be bursted down pretty quick, so maybe you feel like it was on time, but it was too late.