Sooo, I never actually tried any of that, but I have a few build suggestions. Keep in mind though: Leona's passive is a big part of your power budget, and she can't trigger it by herself, so whatever you do, Leona in a solo-lane will always be inferior to a true solo laner that can exploit 100% of its own kit. Maybe it can work out against a late game scaling champ who isn't too oppressive in lane, since once team-fights start you can use your passive, but by this point he should be more useful than you, and you can't shut him down early. And against an early game bully, you simply can't win your lane alone.
Most "standard" play-style, as far as Solo-lane Leona can be called standard, is probably a lot like Malphite/Maokai, and building along those lines:
and maybe a Voidstaff or an Hextech Item last, with Boots in the middle somewhere (either Lucidity for more spells over time or Sorcery for more burst). Other good items to consider are Iceborn Gauntlet (for the spellblade passive adding to your burst), Righteous Glory (for big engages if you didn't go for RoA, otherwise you waste the Catalyst passive), or Frozen Hearth (for the CDR if you didn't built any other mana item). Trinity or Titanic are other good offensive options if you don't want to go for Liandry, and if you are behind, all standard Tank items can be considered depending on the specific circumstances: ZZ'rot, Randuin, Thornmail, Solari, Banner, maybe even Knight's Vow.
Another build, full AP, based on
may work too. Not too sure about Liandry, maybe Protobelt or GLP are better. Obviously you'll be very squishy compared to standard Leona, but still less squishy than a standard mage, and you have a pretty big burst.
You can probably go for a build based on Titanic Hydra, and then other Tank Items with HP, since you have Hydra plus Q aa-resets.
Yet another possibility is an on-hit build, with a potpourri of items among:
and maybe
/
. Buy EITHER Titanic OR Lichbane, and complete your build appropriately with more HP or more AP. Don't forget to exploit your Q aa-reset.
Have fun experimenting.