Fifteen years ago seven Hindu-and/or-Sikh monotheists from Punjab got together and designed a space (kilo)station. They called it "Hyperion" in homage to their Greek cultural roots. The basic design is the torus; which they stack, so as to keep it from tumbling chaotically like the Saturnine moon of that name. They had clearly thought deeply on the topic, and the NSS agreed awarding their proposal a grand prize.
The plan was to put this station at TLL4. As to scale: 900m radius (=1.8km dia), staffed by 18000 people.
As to L4 and not L5: interplanetary dust. We call this the Kordylewski Cloud after its 1961 discoverer and, yes, it is more visible in L5. The authors did not know this at the time but a Magyar crew has verified that L5 captures more dust than L4. This is caused by Terra-Luna-particle not being a perfect Lagrangian system, as the Sun also hits the particle; and that Terra-Luna orbit their barycentre with an eccentricity (Brave AI sez: 0.026 to 0.077, higher than Earth's own) and inclination relative to the Sun. For my part I don't rate this dust-delta as so important.
If we must have a megastructure at our own L4 or L5, and I repeat I am very skeptical, a trio of Japanese evaluated the cost: 20MT of material. If they brought it from Earth even with that fancy Starship they'd be looking at ten million million 2025 dollars and over fifteen millennia (Egyptian history is said to be five of these/a third of that). But the Punjabis probably figured as much which is why they wanted to feed their station from Luna... maybe by coilgun. Nitrogen and phosphour might have to be fed from ambient passing asteroids.
I hadn't noticed Hyperion being referenced much since 2011. Janhunen's dumbbell is smaller so cheaper and safer, for TLL4 (or L5... or L1). Same holds for Orion Ruzicka's reinforced torus if they keep the mad lad in check. Miklavcic's spinning bag of dirt and since-then Jensen's various schemes were always meant for in-situ mulching of asteroids... somewhere else.