Most articles measure input lag from the time you click and button and the time the response appears on the screen, but since in this game you don't really have to react to what is happening on the screen as fast as you can (unless you are trying to play with an AR that is too high for you), in this game, the graphical delay is not really important, just the time between the button press and the game detecting it.
Also, it is important to distinguish between sources of constant lag and sources of random input lag.
Constant lag is not important as long as the player is used to it. If a player keeps using a setup with constant lag, they will automatically adjust to the point where they don't even notice it is there and it won't have negative effects on their performance.
Random lag has more detrimental effects on performance, since the player can't adjust to it.
As long as the BPM of a song is not perfectly synced with the frametime you are playing, and the fps is perfectly constant, the delay caused by frame time each hit is a random variable, following closely an uniform distribution, with an average latency equal to frametime/2, and a standard deviation equal to the frametime/sqrt(12) (for example, if a player has 0ms average hit error and 70 UR on a certain play with very high fps, copying their exact inputs but with a setup that uses 200fps and is the same in all other aspects, it would get around 2.5ms average hit error and 71.47 UR; if the original play was less accurate, the effect would be even smaller, for example, with 5ms average error and 200UR, lowering to 200fps would give you around 7.5ms average error and 200.52 UR). The player can adjust to the average lag caused by long frametime, but the increase in UR can't be adjusted to, so the accuracy achieved in a play is slightly affected negatively, in average.
Stuttering frames (detected in the game client by those squares showing up next to the fps display) with high average fps have a much worse effect on performance than a constant fps that is not high.