Congratulations on the new turntable, good luck getting it set up and working properly. Having the needle ‘jump’ when you put down the lid isn’t abnormal if it’s not done carefully.
The OP was having a problem with tracking and it was being suggested that removing the cover might help. I think that’s all that it was about.
I don’t have any idea if covers up or down make any audible difference. I’ve heard people state it’s better to not use covers, but the evidence seemed anecdotal. This could easily be measured. The only thing I could see as a possibility is if the cover is up, it may throw off a level platter on some of the lighter plinth decks. Again, it’s easy to measure the platter level with the cover up or off to see.
I’m not sure how easy it is to get the turntable back to the dealer to have the set-up checked, but there’s a few things that can be done at home to check it. If I was setting up a new cartridge I would do these in this order. It’s also not a bad idea to check this stuff as not all dealers will take the time to do this set up properly.
1) Check the platter is level in it’s normal location with a small spirit level or bubble level. Make sure that the platter is perfectly level in all directions.
2) The VTF or tracking force has been mentioned and some sort of stylus gauge is a good idea to check that. Cartridge tracking force is measured in grams and will likely have a range. Check with the cartridge manufacturer for appropriate weight.
3) Tonearm height can be checked with a small “recipe card” or another 6x9 card with parallel lines. Place the card behind the tonearm when the stylus is resting on an LP to check that the tonearm is level with the surface.
4) If the cartridge alignment isn’t fixed on the arm, overhang and alignment can be checked by downloading and printing a protractor from here:
https://www.conradhoffman.com/chsw.htm (it’s the third link, titled “Custom arc template generator…” If the included “READ ME” text is followed, a perfectly accurate alignment can be obtained. I print onto photo card stock, tape it onto a cheap LP and fasten the platter with a couple of pieces of painter’s tape. You would need to know the type of alignment that your dealer used to download the correct alignment, i.e.- Loefgren, Stevenson, Baerwald or ‘generic’ (my words) where the stylus is perpendicular at the centre of it’s arc.
5) If azimuth alignment is possible, you can check that with a small mirror resting on the platter and there’s measurement LPs if you want to dial it in perfectly.
6) Recheck the VTF or tracking force.
6) Lastly anti-skate, which I generally set with the tonearm’s guidelines and then check with a test LP.
The surface your turntable sits on may or may not be a factor. A wobbly shelf or cabinet is likely not going to be a good idea. It also depends on your building’s architecture and room set up.
Have fun!