I'll point out, first, that in the referenced post, there's a particular nuance in the Boss/Employee dating relationship that can be more problematic than any relationship between co-workers. While peer-to-peer (or mild variants where there is no direct line of reporting) can still cause endless office drama, they are quite different and some of the liabilities don't apply. Also, the realm of teasing and gossip goes way up when it's just two of the gang, since your peers will find you both safe targets for gentle mocking.
1 - Avoid the perception
It may be too late. If it's gotten into someone's head, it may be there to stay. But at times, the perception can be avoided or reduced by limiting the exclusivity of the relationship and watching your non-verbal cues. Both are fuzzy things, but here's a few ideas:
do have lunch together, but also include others at times. 2 people having lunch together once a week or so isn't a big deal. 2 people having lunch together every day is pretty exclusive.
watch your timing - 2 people disappearing for a 2 hour lunch is a lot different from 2 people having lunch for half an hour in plain view of everyone in the office cafeteria. Those are two extreme cases. The standard out to lunch period in US offices is 1 hour. Plenty of groups take a Friday lunch that pushes into the 1h + 15-30 min range, but if you are gone for 2 hours, some lewd person in office is thinking "quickie (wink, wink)".
be aware of non-verbal cues - I have plenty of male friends (I'm a woman) who I don't mind touching on the arms or giving a big hug to - I don't think of it as romantic, and different cultures have VERY different norms here. But in Corporate America, impersonating Mr. Spock may be a better model for physical contact. It's usually the mismatch of cultural expectations that leads to confusion here.
be aware of husband and wifey behavior - I have seen a number of patterns where a male/female friend pair fall unconsciously into some of the standard husband/wife patterns - for example - the woman nagging the man about his bad diet and lack of exercise. Certainly something I joke with any of my friends about, but when it falls into standard gender patterns it gets misinterpreted, especially if the two are unusually close in how they spend time together.
be aware of overall norms - if you are the only two going out to lunch together, and the rest of the office works through lunch, you're going to get noticed, regardless of any other of these tips.
Overall - it's important to not give up some of the things you actually like about the relationship. There may come a point here where you simply decide that the friendship is good the way it is, and the rest of the world can stuff it. I'd certainly rather see that than to see a good friendship get screwed up by caring too much what other people think.
2 - Response
Awareness usually comes in the form of teasing. The gentleness/craziness is largely a factor of office culture and the dynamics of your team. I usually trust that if I'm hearing it overtly, it's not a big deal - people just like to joke around. The cues I'm most sensitive to are actually the unvoiced cased of awkwardness or withholding, or tacit assumptions that it really is a romantic relationship - these can be a lot harder to see easily than someone simply joking about your "girlfriend".
If what you get is overt joking, and you want it to stop - explain once, seriously, that it isn't true and then show that the mocking doesn't bother you or interest you. A joke generally only keeps going if it's funny, and if you show you are hot under the collar or reactive to being prodded, then it stays funny. I've even seen work "couples" join in the joking, because they were so confident in their friendship that they really didn't mind the teasing - note, this was a case of two independent contributors - neither one aspired to management - at all.
It's harder with the unvoiced issues - it may be time to take aside those displaying the most obvious awkwardness and tell them earnestly that nothing is up. It's usually a case with stuff like this of "try it once, then drop it".