Do lugged frames have an advantage to non lugged or is it just for aesthetics?

Define "advantage" and by who is benefiting from it. One community wants some new buzz with each market cycle. Some want their egos stroked at the start of group rides, with the bike they are on. Factories care about time to complete the build VS the cost to do so. Pick your poison.

Lugs provide a very well established method to support and help position the tubes during the build, provide massive surface area at the joint to allow non welding joining methods be strong enough.

Back when bicycles were considered the height of modern industrial ability (late 1800s) brazing was the usual way to join steel tubes. Welding wasn't anywhere near as "refined" as these days, both tube alloys (as example 531 came about in the 1930s and wasn't considered a weldable alloy then) and filler rods weren't what they are today. So steel structures were often brazed. Fillet brazed joints didn't offer much branding and took some skill and time to look nice. Lugs offered a lot of visual details for branding and worked well for a factory production and cost reduction of joining when done in volume. Over the decades since consumer acceptance has swung from fillet to lugs to welding and now composites with their shapes determined by a mold.

There have been a few published efforts to test different joining methods (of steel tubes) in the last few decades. Bicycling magazine had an article where the commissioned 3 different joining methods and tested the strengths and failure modes (for steel tubes). The 3 joints were lugged, filleted and welded. The failure modes were somewhat different but they all did fail. They all were good enough to work too. Some of this was about where along the tube, from the joint, the HAZ was as this is where the tube strength suffered. Also undercutting, be it from poor welding or heavy filing could come into play. Lugs can hide best mitering and thus become a structural member instead of a filler housing.

Their conclusion was that all 3 methods worked well if done well, could fail is not done well or if the stresses exceeded the designs.

One limiting aspect of lugged use in the last 3 decades, or so, has been the use of more tube diameters and a greater range of tube angles. producing enough lugs at a low enough cost to fit all the geometry and tube size choices has a very high cost. So lug offerings have become fewer, basic economics at play. It is these reasons that some, like me who don't weld, have gone to fillets for much of their work. Yet half the half dozen frames I have built in the last few years have been with self made lugs. Andy

No advantage. Its just a choice that is made for aesthetics or the builders desire to use one joining method over another.

Lugless allows for more freedom in frame geometry, as the builder is not confined by what the lugs allow. Lugs allow for some artistic expression in the tubing joints, within the geometric limits of the lugs.

I know we could all easily lose more weight just by going easy on the donuts etc. etc. but does anyone know roughly how much a set of lugs weighs? I'm just curious about it in the name of science.

A set of 3 lugs can weigh between 80 and 130 grams + -. A investment cast seat lug will include a binder bolt housing that would need to be attached to a fillet brazed or TIG welding frame. I weighed a unfiled Henry James down tube lug at 33 grams and a filed one at 22 grams.

Sometimes on bicycle forums posters will say a TIG welding frame will be lighter than a lugged frame and that is not necessarily true. It is likely the TIG frame is heavier because tubing has to be reinforced by the weld. The easiest way to do that is with an outside butted seat tube and a much heavier wall head tube. Those weigh significantly more than tubes used on a lugged frame.

One place where it is better to use lugs is on heat treated tubing like old Reynolds 753 or Tange Prestige. Lower temperature silver brazed lugs reduce the loss of tensile strength in the heat effected zone compared to bronze brazing. Of course Fillet Pro could be used instead or 853 tubing.

Yes this is a good point about the externally butted ST and thicker HT. The external butt on Columbus STs is 40mm long and adds 1.2mm of wall. I make that 33.9g. Assuming an HT that's 160mm long and 1.2mm wall rather than 1.0 we're adding another 28.6g there resulting in a total of 62.5g.

The main triangle of TIG frame also contains about 17 inches of weld, which weighs about 10g, but idk how that would compare to the very thin but much larger area of the braze in a lugged frame.

So perhaps a TIG frame is still generally lighter than a lugged one but only by a whisker and not if you use lightweight lugs and then file them.

But what about butt length? I think in theory on a TIG frame you can use a tube with shorter butts as the heat doesn't spread that far down the tube. but I don't know if anyone does this. Reynolds and Columbus do seem to supply tubes with either around 75mm as the short butt or about 100mm.

853 is also heat-treated so perhaps there would also be some benefit. It's confusing because it's also "air-hardening" so in some ways benefits from heat. But you can still presumably also lose the heat treatment.

Never underestimate the role that aesthetics plays in purchasing decisions. Not that it's the only thing, but there is a lot about decisions (not just type of joining) that comes down to what you (or I or whoever, and we're all different) thinks looks best.