Can you specify, what lag on what occasions you are referring to? I am not experiencing lag at all.
It helps if you deactivate Super-Wallpaper (Mars/Earth) and speed animations up maybe (dev.options, speeds to x0.5).
May sound silly but worked absolutely fine for me:
I have RedMi Note 9 Pro with MIUI 12. It was dead laggy in the menus.
What I did was I changed Screen Resolution and now it's smooth like butter! Some other users suggested that in some forums, and it works fine.
Go Settings -> Display -> Text size and reduce it to Small.