When I was attending my stuffy, private all girls’ school back in the 80s, biros/ballpoint pens were strictly verboten - essays were to be written in fountain pen or risk rejection. I feel rather wistful for those days, and dislike biros to this day. Nasty, thin shafted things, give me hand cramps.
So, what was it like at the turn of the 20th century?
A pen doesn’t have a top or bottom. It has a tip or point.
When stored, the tip of a felt pen or ballpoint pen would be stored down.
I don’t remember the correct way to store a cartridge or inkwell pen, though I’m old enough to have used them. I’m glad they’re history, since I ruined enough stuff when they leaked.
This Brit has never called the cap of a pen a lid, nor ever heard anyone else do so that I can recall. I might sometimes just call it a top.
I too have never heard a pen cap called a ‘lid’.
(I’ve lived and taught for decades in both London and the Midlands.)
Sanvito, which part of the UK are you from?
Funnily enough, I grew up in Birmingham and have spent my adult life in London. Pretty surprised you haven’t heard of lid - a google search shows it on numerous sites, I haven’t made it up!
Kind of ‘dating’ yourself there, ain’t you, Siam Sam? 
(bolding mine)
You and me, both, sahirnee! 
(And apparently Siam Sam, too. :p)
No, it costs quite a bit more these days. 
Bummer. 
Pens have a cap in my opinion, but if you want to call it a lid, or something else, this is fine and nobody should make a big deal.
I guess that depends on your definition of “stored.” If I put a pen in a breast pocket, with the clip over the pocket edge, is that “storing”? If so, on my desk right now, I have a Sharpie (fiber, not felt) that would then have the point up. And I have a Bic Round Stic (ballpoint) that would also have the point up.
If the pen has a detachable point cover (not gonna enter this argument), then it would have the point up if clipped to a pocket. If the pen does not have a detachable point cover (a retractable), then the point would be down.
Now I have to get back to work – something less important, like rocket surgery.
Fair enough - a quick Google does indeed show there are images for pen ‘tops’, pen ‘caps’ and pen ‘lids’.
(It still doesn’t fit with my idea of a ‘lid’, though!)
I voted “caps”. I’ve never heard it called a lid; could it be a difference between American and Canadian English?
I voted “cap”.
Pens ensues.
I don’t really call it a lid anymore, but I do remember calling it a “pen lid” when I was younger. Though, for all I know, that’s confabulation. I do know that “pen cap” sounds weird.