The input lag is from the display's processing capability. The stated input lag numbers for displays usually only apply to when you feed it the exact native resolution. If you output a 1080p signal to a 4k TV, it has to upscale the image which means more processing. This could triple the input lag.
On TVs (instead of monitors), they often have a game mode with minimal processing (eg no frame interpolation). I only get the lowest advertised input lag on my LG oled on game mode and only if I feed it it's native res. If I use cinema mode or feed it a 1080p signal, that 20-30ms lag becomes 70-100+ms.
There is nothing you can do to get lower input lag than the manufacturers stated lowest lag specs for a display.
I don't quite understand the question. Both of these monitors have a 1ms response time and a 144hz+ refresh rate. The VG259QM is 1920x1080 and surely if you're looking to purchase a $300 monitor you're not looking to run a resolution lower than 1080p. If you feed either display its native resolution you will have a 1ms response time and a minimum refresh rate of 144hz. If you're only going to run 60hz then why are you going to get a monitor that supports a hugely higher refresh rate?