So how did that machine work?
Delousing machines in the Great War were usually steam machines.
https://rnzaoc.com/2017/03/14/mobile-laundry-and-bath-equipment-1941-1990s/
My search turned up a lot of stuff about it being a problem in the great wars, but urban Rome is a very a different beast, with much less science and much more leisure time and stability.
Not so sure about much more leisure time. Working class Romans would have been working sunup to sundown, while soldiers always have to fight long stretches of boredom, even in the chaos of the trenches.
My first instinct is boiling water. The Romans would definitely have tried that, and few things can survive it, but I’d also guess their textiles wouldn’t have survived well. My next thought is smoke, which I guess they could have just missed, but then again maybe they’re resistant to it. The eggs at least wouldn’t need to actively respire much. Salt maybe? Tiny things don’t generally deal well with the wrong salt concentrations.
Nit combs and oil rubs were the usual treatments. The oil can asphyxiate the bastards so you can catch them, but most’ll start breathing again after a while, so you still have to remove and dispose of them manually.
Did most (urban, non-deployed) Romans have time to go to the baths, at least? I kind of figured it was universal, albeit with some kind of internal segregation like the Colosseum, but I’m realising I don’t actually know that.
The baths, sure, but bathing won’t kill lice. They can go without air for up to 10 hours. Tenacious things.
Romans would generally go to the baths daily or every other day (depending on the city/time period). Some baths were free to the public (or had hours/days that were free to the public), while others were admission by fee or connections only. I don’t think there was any segregation - no class segregation at least; gender segregation, sometimes. It varied. Often men and women would bathe together; some cities the baths would have separate rooms for men and women; and other times the baths would set aside different hours for men and women to bathe.
EDIT: Just to clarify what I meant about leisure time and ancient Rome - I don’t mean to imply working-class urban Romans had NO leisure time on a daily basis, only that comparing them to WW1 soldiers, with the mixture of military scheduling and long stretches of boredom vs. a long work day, there’s probably a broad similarity in how much ‘sit down and hunt lice’ leisure time they had.