There’s no difference between bravura and lazy. They do identical things, just flavoured slightly differently.
Way off base.
Even mechanically, they were quite distinct:
A bravura build was high-STR, with enhanced defense and strong offense in its own right. Exploits it's particularly good at invited attacks, protected allies, and even marked - and if they keyed off a secondary stat, typically used CHA.
A lazy build would put lower-priority on - even intentionally dump - STR and offense in general - the powers it was best at tended to key off INT, and obviously, to grant attacks and other actions or provide comparatively passive benefits.
Not really. In one you attack and cause a rider. In the other you give up the attack to cause a rider.
That's a gross oversimplification often used in the edition war to criticize 4e class designs, in general. Yeah, 4e simplified things down to attack rolls to resolve all attacks, instead of using saving throws and one-off mechanics. That didn't render any two given 'builds' (really alternate feature choices: the 4e equivalent of a 5e sub-class) the same any more than it rendered all classes the same.
It'd be like saying there's no difference between the 5e Cleric and the 5e Warlock because they both cast spells. By that standard, most 5e classes have no standing to exist.
Aside: One mildly annoying thing WotC sometimes does is to take terms widely used in the community - like 'exploit' and 'build' and even 'Core' and give them an official meaning somewhat at odds with that usage. 4e called a choice of a defining class feature that could ripple through the class's capabilities and powers from 1st through 30th, a 'build.' Essentials called an alternate version of a class with often radically different mechanics and role, a sub-class. 5e calls a set of alternate class features a sub-class (or in the case of martial classes, an archetype). Archetype actually means something in natural language, too, but 5e departed from it's jargon-avoidance long enough to co-opt it. :shrug:
Anyway, upshot is that the 6 official Warlord 'builds' (and the Archer warlord) were more like 5e sub-classes than char-op builds...
Lazy lord isn’t an archetype. It’s just a way you could play any tactical or inspirational warlord.
"Lazylord" was a build in the CharOp sense. You could use it as an archetypal imperious commander barking out orders, or a stereotypical plucky side-kick shouting encouragement, or a 'victim' (because damsel in distress would be sexist) inviting rescue. Where it really shone, IMHO, was in the latter sorts of concepts, they're something you've never been able to do in D&D without simply being useless.
In the first case, the imperious commander shouting orders, sure, tactical builds could do it, too. (Technically, because the Lazylord was a charop build, it used some official-build's toys, too, typically the Tactical warlord, though Resourceful could work, too - it just wasn't a big part of the build - in fact, had it been an official build, it probably would have granted allies extra actions when they spent action points, with it's own 'lazy presence').
Anyway, if the warlord design is as flexible as it probably should be to be a functional support character, any given warlord probably could use a gambit emblematic of any given other warlord archetype - including gambits that whatever less flippant label we put on Lazy (I like "Icon") is best at using.
The idea that one sub-class being able to use another's tricks somehow invalidates both is absurd on the face of it in the context of 5e. Look at the Wizard Traditions, any wizard of any Tradition can cast spells from any other's bailiwick, just like that. By the standard you've constructed for the Warlord, the Wizard has literally no valid sub-classes, and is not fit for inclusion as a full class.
Same's true of most sub-classes really.
Honestly, the same is true of every objection to including the Warlord as a class - were they applied even-handedly, they'd eliminate half the extant classes.