If the game created a new le_graphicsmanager.ini correctly, it should be set on Medium quality @ your default Windows res, with framerate limiting on 60fps (and enabled) and vsync off… I am assuming that you removed the file while the game was not running?
If the game didnt reset to that then something is definitely odd here…
Again, info is lacking in that you dont say if you are playing the game via Steam or standalone, so I am going to assume Steam - if this is the case, then please run the game verification process in Steam to make sure your installation has actually run properly to tick this off the list as a possible cause of your troubles.
Side note: Sometimes the settings UI can get a little borked and you have to toggle a setting, close the menu and reopen it to double check that it actually changed. This doesnt usually happen on normal graphics settings but its obvious something is odd on your setup so anything is possible.
Also, if you have any driver level overrides, then that will ignore any in-game settings and based on your description of whats happening its very important that you check the driver settings to see what is taking priority.
The framerate limiting (with enable checkbox) in the in-game settings window is exactly what you are meant to use to do this - its there for this specific purpose and works perfectly for this normally… Its what most of us use while the game is in beta/unoptimised to get the best compromise between performace/stability/quality.
Honestly dont recall anyone having this kind of issue where graphics settings are ignored and I have been helping out here for almost 2 years… There has to be something overriding or even ignoring the game settings. The game wouldnt be shooting up to 250fps if vsync was working properly AND/OR it was correctly reading the enabled framerate limit in-game. It simply doesnt do that.
And yes, there is no need for 250fps in a game like LE… in fact, imho, anything more than 100fps is pointless from a gameplay perspective as there is no need for millisecond first person shooter interactions… Some people argue for smoother animation, but honestly once you get to a certain point anymore fps is just wasted.
The files I recommended you include would help - its very hard to guess or assume things that would be simply answered by the info they contain.