A Batlantern meet cute, except it's out of costume. Pre-Identity reveal.
Hal Jordan is visiting Gotham, because he's not allowed to when he's Green Lantern, as a mental 'gotcha!' towards mr-getoutofmycity Batman ( + basic tourism, they have the best pizza places after all)
Then, of course, he's lost. The streets of Gotham are a natural labyrinth where google maps hasn't fully rendered it. And so he had grabbed a physical map, old fashioned, but it did the work.
Until he got to a specific district, rapidly developed and not up to date in the map he got. He winged it, following where people were going, and ended up in some random opening event.
Deciding he does not want to waste his morning there, he approaches the first person he sees, tall dark and elegant features register in Hal's head, but after tapping his shoulder he looks down at his map.
Bruce Wayne turns around, and sees a handsome brunette looking down at a map like it's the 1800's, lost in a city where looking slightly distracted WILL get your wallet stolen, asking him if he knows how to get the hell out of this boring event, not seemingly aware he's talking to both the main attraction of said event and Bruce fucking Wayne.
He's smitten immediately, offering his best advice on how to navigate the city, he takes a pen out of his suit and draws around the "can't miss" spots of the city, proud to show it off. Hal nods and jokes with him a bit, his "so, come here often?" gets a genuine snort out of Bruce.
He glances at the event, and decides he'll probably have a better time with the man, he walks Hal around Gotham that morning, they get coffee, and talk about their lives, all the while trying to not tell the other too much (I'm a pilot instead of a superhero vs I'm a business man instead of The Wayne/vigilante)
They get an alert on their coms, they have an JL meeting in five minutes, so they give eachother their phones and plan on going-
But then, they keep walking towards the same direction.
But it's not awkward! They laugh and just keep making conversation, silently happy they get some extra minutes together.
Then, they get to the same teleporter to get back at the JL base...
Hal freaks out, Does Bruce know? Or Is he just following him unaware of where they were going?
Bruce scans in his brain who Hal could be, if indeed he's here for the same reason, it doesn't take much time, he sighs and just gets in, "Not a word, Lantern, not a word"
Hal is both proud and horrified he's the first to know Batman's identity, especially after searching who Bruce Wayne is. But he really wanted to keep talking to Bruce...
Bruce is mourning his meet cute.