I have been asked many times whom I would swap for whom if I was running a Lost Lands adventure set in Paizo's Golarion campaign world. I've always run Lost Lands stuff "as is" so it had never come up for me to sit down to look and see how I would do it. Also with our Lost Lands pantheons of deities in constant flux as I add, edit, and rearrange based on the many prior Necromancer Games and Frog God Games products, the project just always seemed too daunting. However, I believe the Lost Lands pantheons are probably 90% or more finalized at this point. Pretty much all the common deities are done from the Hyperborean and Foerdewaith pantheons, the non-human deities are for the most part done, and I've even reached back into prehistoric cultures to build founding pantheons. Really the only big thing left is finalizing our pantheon for the Old Way (that is, the early Celtic-style pantheon of the Ancient Ones who once inhabited Akados). Other than that there's still some work to be done on exotic pantheons of distant Libynos and some Asian-flavored pantheons of the Xi'en Hegemony, but those won't have much effect for just the core Golarion deities for the most part.
So as the final days of my summer wane and I've managed to get through most of the projects I had on my plate to finish before August, I decided to sit down and work out the conversions I would do if I was to run Slumbering Tsar or something, set in Golarion. Of course, this is all highly unofficial. The Golarion deities are the intellectual property of Paizo, Inc., and we at Frog God Games have no rights or access to them, so this is really nothing more than a theoretical exercise that will hopefully be of use to some gamers who would like to use this kind of crossover in their home games but don't have access to the complete (or at least 90% complete) roll of Lost Lands gods. This is for those guys (and in no way constitutes a challenge to Paizo's ownership and use of the Golarion deities). Some Paizo gods have multiple varied aspects that I'd divide between different Lost Lands gods--for instance Calistria is the main goddess of elves, plus a goddess of revenge, plus a goddess of sensuality/lust. So I'd apply 3 different Lost Lands deities to that and convert all references to Darach-Albith, Moccavallo, and Bast to Calistria in such a game. The same kind of thing applies to Norgorber who literally has four different cults.
Special thanks to Frog God Games writer and Pathfinder converter Jeff Swank for motivating me to sit down and make this list. For the record, he worked on Quests of Doom as a Pathfinder converter and did not get credited (for which I am both highly embarrassed and deeply sorry), so I wanted to give him a shout out. He's also written couple of our new line of Lost Lore pdfs, so check those out when you get a chance for some cheap, bite-sized, but cool bits of Lost Lands crunch.
So without further ado, here's how I would make the swaps for my own game if I was to run Lost Lands adventures in Golarion:
Abadar = Thyr (order, justice)/Sefagreth (business, banking)
Asmodeus = Hecate (magic)/Asmodeus (rulership of Hell)
Calistria = Darach-Albith (elves)/Moccavallo (trickery, revenge)/Bast (sensuality, lust)
Cayden Cailean = Pekko (also Snorri Horrnison for dwarves of Clan Targ)
Desna = Tykee
Erastil = Freya
Gorum = Bowbe (Gromm the Thunderer would also fit pretty well)
Gozreh = Telophus (nature, weather, seasons)/Quell (the seas)
Iomedae = Muir
Irori = Belon the Wise (loses the martial aspect but keeps the traveler and mysterious foreign traveler bits)
Lamashtu = Tiamat (the Primeval Mother really fits the role of Lamashtu)
Nethys = Jamboor (mysterious spooky magic with just a hint of death thrown in for flavor)
Norgorber: Blackfingers = Set/Father Skinsaw = Orcus/The Gray Master = Mirkeer/The Reaper of Reputation = Grox
Pharasma = Da-Jin
Rovagug = Dajobas
Sarenrae = Mitra
Shelyn = Zadastha
Torag = Dwerfater
Urgathoa = Hel
Zon-Kuthon = Demogorgon (not just the traditional demon lord aspect owned by WotC - see Mountains of Madness to see the cool stuff we're doing with ol' Two-Heads)
Achaekek = Rachiss
Gogunta = Tsathogga
Razmir = Nergal (particularly his dominance over the mysterious Huun Imperium to be explored in future Lost Lands products)
Aroden = Arden
That covers all the major Golarion gods (of Avistan, at least) and some of the important minor gods. If there are any other obscure or minor gods that you'd like to see an unofficial Lost Lands take on, post it in the comments and I'll check on it occasionally to see what's what and if I can come up with a good substitute.