I've never been to LF, I understand that it is close to DH.
Unless things have changed in the year and a bit since I've been to DH, the only signage that exists is very nondescript and is in no way indicative of the type of business operating on the premises (I suspect it only exists at all so that the admin can give clients at landmark to look out for in the 'come on up' text).
Infact any of the NZ run establishments that I've gone to are either nondescriptively signaged or have no signage at all, so it isn't like you're walking up to a doorway that has a 20ft tall 'Girls, Girls, Girls' neon sign.
Therefore a casual passerby who sees you going through any of these doorways will have zero idea what you are about to get up to, most people are not particularly observant about anything going on around them that isn't directly related to them, so probably don't even register that you're there at all they're too busy caught up in whatever they have going on unless you are particularly notable in some way (either appearance or actions).
Anyone that has been there will know, but they are hardly likely to come up to you and say anything as they want discretion as much as you.
Which only leaves someone you know spotting you in an area that you either shouldn't be because you are supposed to be 5km away in an office or something, or a time you shouldn't be loose on the streets, and either coming up to you to talk or mentioning it to someone you didn't want to know that you were out somewhere (ie: a partner most likely).
In which case, your discretion is sunk no matter what, and you would be well served to have some form plausible excuse handy, researched and practiced in your head so that it comes out naturally.
Or just not go during the day.
Although I'd have thought that would be easier during the day and less likely to require some elaborate reason for being out than in the evening, especially in the areas of DH, LF, SB or TA, as a general rule.
I don't get the panic about some random seeing you on a street going through a random doorway with signage that does not indicate where you are going or what you are up to, although I do get the desire for discretion (but clearly so do the agencies).
So unless you're wearing a t-shirt with a print saying 'look at me, I'm walking through a doorway to go bang a hooker', I think you have very little to actually be worried about ... that said, if someone was wearing that t-shirt most people wouldn't believe it any way and would pass it off as a joke or novelty thing (if they noticed you at all).
My technique is just to walk up to the doorway and step through carrying an attitude like I own the building (I look and dress like a redneck, so the least likely person to own anything more than a Ford Ranger), and nobody around ever bats an eyelid, if they see me at all.
It isn't like you're trying to pass secret documents off to a Russian spy, so your OpSec doesn't need to be that detailed or paranoid.
IMHO
(slight edit for sort of comedic effect: On the subject of passing secret information to a Russian spy, seeing a WG would be a pretty good way to do it as it would be hard for NZSIS to witness it happening and take photos for evidence. Perhaps our inhouse Russian vixen
@NatashaPetrova could offer a new fantasy service where she plays the spy. Sorry Natasha, not being dodgy, just an early morning idea that popped into my head, hopefully you took it in the manner that was meant.

)