How about this:
In a TL in which LTA craft tech reaches early 20th century levels by the 1880s (at the latest) Alfred Thayer Mahan follows up his book "The Influence of Sea Power upon History" with another supporting the use of airships. The influence that he and his original book may then give greater influence to the use of airships.
I have being a spoil sport, but here I go again. The problem is its hard to imagine LTA technology reaching early 20th Century levels in the 1880's - which I still would argue needs advances in aluminum metallurgy and petrol or Diesel engines. One must always be a bit critical when considering the sucesses attributed to some of the early pressure airships of the mid-late 19th century. Often the accounts are more in the nature of sales pitches for a small and only marginally successful prototype, and a whole cottage industry of success stories can grow up over the years when in fact the craft never flew, or at best made inconclusive directed flights in absolutely still conditions/indoors (Or was actually the tiny unmanned gasbag in the photo of the
Avitor Hermes Jr, when the published print turns it into a streamlined hybrid airship with an internal steam engine sailing majestically through the sky). Another case is the
Aeron (the three-hulled unpowered dirigible also shown in your attachment). If you read John Toland's exciting but not always accurate history of airships, you will learn about tests of the
Aeron prototype in front of Abraham Lincoln and a raft of US Government folks, who were amazed that a completely unpowered ship could achieve directed flight merely by using a shifting weight to undulate through the air. It's really a cool idea, but if it really worked or had any future you would have seen Aerons filling the sky by the 1870's. Problem is, there is no incontrovertable documentary record that any of this occurred, or that a flying
Aeron even existed.
Regarding Mahan, I'm not sure he would have been all that excited about airships, even if effective ships were invented 20 years earlier. To him sea power meant the ability to marshall big fleets of big ships. He might see airships as useful scouts...but then so were cruisers and other light, fast ships.