TCC seems to indicate very clearly that Madame Lulu is the reason Count Olaf was able to find the Baudelaires from TRR to THH. However, in TPP, it's revealed that Justice Strauss's colleagues are friends with Count Olaf, and were passing information onto him: “Justice Strauss,” Violet said, “your fellow judges on the High Court are associates of Count Olaf. Those villains will never put Olaf in jail.”
“It can't be!” Justice Strauss gasped. “I've known them for years! I've told them everything that was happening to you children, and they were always very interested!”
“Of course they were interested, you fool,” Count Olaf said. “They passed along all that information to me, so I could catch up with the orphans! You've been helping me all along, without even knowing it! Ha!”
This makes it sound like Justice Strauss's colleagues may have been the ones helping Olaf find the Baudelaires.
Or was it them in addition to Madame Lulu? When the Baudelaires search Madame Lulu's library, they find a photograph of themselves on Damocles Dock, themselves on a list of Prufrock Preparatory School students, and a newspaper announcing that the town of V.F.D. would be raising them, which would explain how Olaf found them in TWW, TAA, and TVV. Esme probably just told Olaf that she and Jerome would be adopting the Baudelaires in TEE, but could Justice Strauss's colleagues be the reason Count Olaf found them in TRR, TMM, and THH?
The evidence tying Madame Lulu's research to Olaf's pursuit of the orphans is far stronger than that of the sinister judges. Maybe they, thanks to Justice Strauss, were able to give Olaf other kinds of information - on their allies or other activities, perhaps? Or the Baudelaires' location in TGG and TPP, after Olivia was no longer able to assist?
I've never liked that reveal in TPP because it does seem redundant when we already have Lulu as the explanation for how Olaf finds the children. However, the judges seem better placed to learn where the Baudelaires are - Lulu is living out in the Hinterlands and I think I'm already a little skeptical when it comes to the idea of her stumbling across the three pieces of evidence you mention.
I don't really see what information would be of use to Olaf other than the Baudelaires' current guardian, and Olaf specifically says "so I could catch up to the orphans", implying the sinister duo were informing him of the children's location. Their help seems to have been going on longer than since TSS, as Strauss says "they were always very interested" and it seems to me that she's talking about a longstanding situation rather than information she let slip a couple of days ago.
When it comes to Olaf finding the Baudelaires in THH, the owner of the Last Chance General Store knows that the children were in his store, and may have eventually realised that they escaped by joining the Volunteers Fighting Disease - somehow this information could have made its way to Lulu, the sinister duo or Olaf directly, perhaps with the police or Mr. Poe as middle men. Or the telegram the Baudelaires sent could have been a lead for someone who was searching for the Baudelaires.