In patch 7.22, League of Legends implemented a leveling system to replace their previous system that capped the level at 30. With this new system, there is no level cap and the player's account level will continue infinitely.
When attempting to estimate the speed at which a player levels up, according to the League of Legends Wikia,
Estimating the required time to level up can be done by taking one's level and noting its position beyond a multiple of 25 (except for the first two progressions: 1 to 30, and 31 to 50). Example: Leveling from 51 to 52 is faster than leveling 74 to 75, but also quicker than a player at level 49, since you're positioned at the very first level of the count (51 to 75).
However, I have been unable to find any site that references any sort of experience required plateau that a player may reach when leveling up their account. So my question is, is there any sort of plateau that a player will reach, or will the experience required to level up a player's account just increase infinitely?
Edit: It was brought up to me that the Leveling Up section in the Wikia linked earlier also contains a graph that includes the XP needed to reach the next level. Unfortunately, once the higher levels are reached in the graph, the XP needed just changes to question marks. So it may be the case that nobody knows for sure.
Best Answer
The required experience needed per level goes through a "staircase effect" depending on where your progress to the next milestone level is.
In the above graph, the blue line represent the leveling curve as initially released during the preseason, and the orange line is the updated (current) leveling curve. As you can see, in the old system the staircase gradually moved higher and higher until about level 150, where the "staircase of difficulty" for leveling up plateaued. In the new system, the staircase plateaus much earlier, at level 50.
Source (Check section: "The 30-and-beyond leveling curve")