I disagree,
I think that the Brusilov Offensive could cause the collapse of A-H, however it would be a whole lot easier if the POD is a few months before the Lake Naroch offensive. Had the Russians focused on capturing Lemburg instead of Kowel, the Austrians would have been completely unable to resist the attack. Brusilov made another error in changing his tactics after the first attack. After the Germans began sending more reinforcements south, the Russians stopped using the infiltration tactics that made the first wave so successful and returned to the mass infantry charges which depleted the forces.
Brusilov was told that there would be absolutely no reinforcements, no additional shells, and an offensive in the north. He based much his attacks on the Idea that a mass offensive would be launched simultaneously. Had he known that the offensive was mostly on its own for the summer, he would not have focused on targets which only made it simpler for the northern offensive.
Lets say that Evert and whoever Kurpatkin's successor was, I cant remember his name off the top of my head, had attacked on time, the chances are that the offensive might have reached its goals. Now had Brusilov been told that his offensive would be the only one, then he would have changed his goals, and once the Russians reach the Carpathian mountains, the Hungarians won't continue the war. If Hungary demands a peace, before the Russians attack across the paths into Hungary proper and before the Romanians join and threaten Transylvania, then A-H will ask for Terms.
So is there a northern attack or not? You suggest both here, which means radically different scenarios. Going with your main suggestion that there is none planned and Brusilov is the main attack, fully supported and told so by STAVKA opens up a massive can of butterflies. OTL the reason that AH intelligence didn't set off warning bells about the attack is that it wasn't reinforced. Believing their defenses were solid, the AH thought they could handle an offensive from just the Southwest Front. If Russian troops, supplies, and artillery start to come in, then everyone knows what is happening, just as OTL and respond accordingly. That means the Germans come in and Conrad is probably forced to stop his offensive against Italy early, if it even happens at all. Actually, this might be worse for the Russians, as OTL success only happened because Conrad stripped the Eastern Front to the bone, in men, supplies, and artillery for his Italian offensive. If the Russians are organizing for a major push then he will be forced to deal with it. OTL he believed the defenses were up to snuff for a simple Front attack by the Russians, but if they were getting ready for a major push, he would have made the Eastern Front a priority.
So there are two options for the Russians, either plan launch two attacks, which they kind of have to do for the French (they can't just focus on the AHs while Verdun is going on), which means OTL plays out the same, as Brusilov is expected to support the northern attack, or Brusilov is the main offensive, which means German reinforcements from the north and no Italian offensive, so the AH forces in the East are twice as strong as OTL.
Either way neither scenario results in AH knocked out of the war.
And to your Lemberg option, which is doubtful if there is still a planned northern attack, it is still 60 miles away while OTL the Russians only made it 45 miles deep toward Kowel. It won't cave in the AH front anymore than the Kowel attack did, and leaves a major salient in the center, which would be ripe for a flank attack from the north.
OTL the Russians made it to the Carpathians, something a Lemberg attack won't do, and it didn't knock out the AHs. The only way the Russians could force them from the war would be to get a full army into the Hungary plain, something they had neither the logistics or men to pull off in 1916.