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.