No it won’t. Lexmark probably priced the cheaper variety as high as they possibly could (without hurting the volume sold) and tried to charge a premium for the “priviledge” to refill the cartridges.
All this is gonna do is short term hit on their bottom line. It might force em to cut cost somewhere at some point down the line. Hard to see where that will come from as that stuff is already sourced dirt cheap somewhere in China. This might even godforbid make em invest in real innovation.