I have always taken the cover off. The rationale is to avoid vibration when closing it or worse case scenario the cover slamming down.
Turntable lid up or off?
My Pro-Ject Classic turntable came with a dust cover. I usually spin vinyl with the cover completely removed and never closed. Does it matter if the cover is just up or fully removed? The ultimate test is just listening, but I cannot detect a difference between either mode (up or completely off).