To anyone that may or might encounter this problem, I actually solved mine.
The problem is that, the USB connector for Nintendo Switch is busted. It doesn't receive too much power that's why when it's docked, it's really slow and laggy due to not enough power being transferred. I had to bring my Switch to the repair shop and thankfully enough, they were able to fix it. Both Handheld and Docked mode are working flawlessly without lags or hiccups.
The problem is that, the USB connector for Nintendo Switch is busted. It doesn't receive too much power that's why when it's docked, it's really slow and laggy due to not enough power being transferred. I had to bring my Switch to the repair shop and thankfully enough, they were able to fix it. Both Handheld and Docked mode are working flawlessly without lags or hiccups.