Many bars (and hotel lobbies) will add a lemon wedge to the top of a glass of soda; often it's used to differentiate between Diet Coke (gets the lemon) and regular Coke (no lemon).
Does this pose a kashrus problem?
And a warning: if you're trying to impress your date by just quoting my answer here, there's a decent chance she's seen it too by now, so nice try. (But then again, if you're both yodeyans, you're off to a good start ...)
Here are the issues, as I understand them and as I've heard:
Lemons are, according to some, a davar charif. The assumption is that a knife cut can transfer into the thickness of a lemon slice not only what's on the outside of the knife, but even what is absorbed in the knife- even taste that is lifgam (24 hours old), the sharp taste makes it lishvach.
The Shach limits the transfer to what's in the knife's outer edge, since lemons are not so strong.
The Rema permits lemons that come in a barrel, if such is the minhag. The Shach says that it's base on the following leniencies:
Some say only turnips (and one other veggie, I forgot which) are davar charif
Some say it can't turn p'gam lishvach
Lemons are weak even as far as a davar charif and after the first two lemons worked the outer taste of the knife, the lemon doesn't have the power to get any more taste out, and those two lemons are battel in the other lemons in the barrel
The cutter may have been using purely designated knives
Hotel lounges may not have the last 2 requisites, although, as Shalom said, a bar may be different. Since we Ashkenazim hold chanan by reg. issur, 60x the lemon seems like a lot of soda in the glass. (60x would be the maximum even if you can taste the lemon after 60 (avidi letaima) since your only machmir by chanan to what's absorbed).
The Maharsham (YD 96:1) holds that by a normal davar charif we go after rov tashmisho - the majority of its usage. Meaning, if most of the time the knife in question is used for cold (non kli rishon) things or for hot but kosher things, then it will not render a davar charif non-kosher, even if sometimes it is used to cut non-kosher meat straight off the fire. This Maharsham has been cited to me lehalacha by a very mainstream rabbi. I think it is clear that any knife being used to cut lemons will fall into this category.