I've been getting a lot of batlantern content on my page and while it is not specifically something I'm interested in romantically, I just realized the potential of platonic batlantern.
Bruce is curious by nature and basically a sponge for knowledge. Hal is barely on Earth and basically a treasure trove of intergalactic lore.
I can imagine Hal spending so much time in space that Bruce's billionaire playboy persona does not have the same effect on him. (tapping the famous "Who the hell is Bruce Wayne" quote).
Works especially well if Bruce is not that outgoing with the team, or is on more of a part time status. The rest are actually a bit confused by the difference between him an his Brucie persona.
~
Batman would be analyzing something or another on a tablet in the common room, keeping to himself and in strolls Hal, loud and rambunctious. His eyes fall on Bats and he makes a beeline for him. "Spooky! I bring enrichment!" He proclaims and drops a data disc in front of Bruce before dropping in the seat next to him. "It's a collection of Quadrant Four literature. Most common languages." He grins, ear to ear. "A thank you for that hint on that political snafu."
To everyone's surprise, Bruce picks up the disc and turns it on all sides. "You don't need a translator, do you?" Hal asks and Bruce just hums, putting the disc in one of his pouches. "I wanted to clear one from Oa but the ambassador mentioned a lot of the languages have Dircheian as a basis. That's the one you wanted to practice, no?"
Bruce humms again and nods. "We're up to 40%"
Hal raises his eyebrows and lets out a surprised whistle. "Man, I was hoping to get some rest, not jump into lantern business as soon as I make it home."
"Technically it's Gotham business." Batman tilts his head and Hal clicks his tongue.
"It was Gotham business 39 percents ago!"
"I'm not going to have a glowstick ruin three months of stakeout."
"I can be subtle!"
The two exit the watchtower common room while bickering and a week or so after, news comes of and alien weapons smuggling ring being dismantled in Gotham.
Another would be Bruce again working on something and Hal just yapping away about some missions, with Bruce just humming every now and again. At one point Hal produces a construct that looks like a tablet with an inscription and Clark recognizes the writing as Kryptonian. What he doesn't expect is for Bruce to look over it and go "Ah, I see what you mean. It would be easy for a therian to interpret that as 'stealing'" and he does a double take because since when does Batman know Kryptonian?
Obviously my personal preference is for this to somehow evolve into superbat with Bruce maybe having a bit of a crush on Clark (or jsut being in a bit of an awe about him) but him being just a coworker. Or worse, the billionaire going through some kind of early midlife crisis. But I could totally see Bruce and Hall playing off each other.