Lanterns of Equestria contains examples of the following tropes:
Adult Fear: Tootsie Flute falls in a river and is nearly dashed against the rocks before Applejack saves her.
Authority Equals Asskicking: The Prime Lanterns (at present Twilight, Rainbow Dash, Applejack, Fluttershy, and Rarity), due to having the most experience with them and representing their group the best, are also the most powerful. Best shown when while saving Trixie from some vengeful Red Lanterns, Rarity curbstomps four of them by herself.
Bait and Switch: The teens Dead Ringer, Monster Bait, and Weekly Victim are set up to seem like they're going to be attacked by a Black Lantern (with one of the teens trying to scare another with a zombie mask), but even though a Black Lantern does show up, it's several hours after they left, and it heads in the opposite direction.
Horror Hunger: The orange light fills its host with constant, ravenous, endless hunger. Apple Bloom starts to exhibit this after she claims the orange ring, becoming able to eat more than her whole family does at each meal. The ‘hunger’ also affects those very close to her physically or when she is using her orange power ring.
Body Snatcher: Though her construct lanterns are not intended to fool anyone, they're capable of everything their stolen identities could do in life. Apple Bloom demonstrates this ability on two sneak thieves she ketches stealing apples from the family farm.
Break the Cutie: The Black Lantern attack on Sweet Apple Acres does this to Applejack, in part because her dead family and Zecora are among the Black Lanterns. The sight of Black Lantern Zecora also does this to Apple Bloom.
Bullying a Dragon: Diamond Tiara and Silver Spoon pick on the now Red Lantern Scootaloo. While she couldn't have known HOW powerful she'd become, the fact Scootaloo was presently drooling flaming plasma and clearly a bit on the unstable side should've indicated this was a bad idea. If it weren't for Apple Bloom and Sweetie Belle shielding them, Scootaloo would've killed them.
Treasure Room: Apple Bloom owns one a ‘hoard’ that she is hiding from her family after they make it plain they will do something about it. It contains both valuable and sentimental objects that she refuses to part with. She is constantly looking to add to it in any way she can.
Dark Is Not Evil: The Yellow Lantern Corp. Despite running on Fear and later containing literal monsters, it's still lead by Twilight Sparkle and firmly on the good side. While more brutal, the Red Lanterns are still firmly good guys as well, in part due to Rainbow's Element of Loyalty helping keep their Unstoppable Rage in check.
Dramatic Irony: Bon-Bon doesn't believe in the Sass-Squash, who was met offscreen by a teenager earlier in the same chapter.
Emergency Transformation: Scootaloo is made a Red Lantern to save her life after an attack by the Black Lanterns. Rarity later had to transform Diamond into an Indigo Lantern after Scootaloo nearly killed her in her rage.
Trixie was inducted into the Yellow Lanterns to protect her from Rainbow's wrath.
The Empath: The Indigo Herd are all this, but Rarity was already naturally compassionate, hence why she was chosen as the Prime Lantern. The Ring just boosts it.
Empty Shell: Apple Bloom's victims are left alive after their identities are stolen, but they don't have their cutie marks and are non-responsive.
Fallen Hero: Commander Hurricane was this even before his death, according to the story Rainbow Dash tells Scootaloo — he couldn't adjust properly to the changes brought about by peace and unity between the tribes, and took to attacking villages incognito to fulfill his craving for battle. When his actions were discovered, he was forced into exile, where he died alone.
Chancellor Puddinghead and Smart Cookie also become Black Lanterns, though in there case it's not them so much as the Black controlling their bodies.
Heel-Face Brainwashing: The Indigo Herd works this way by (except for Rarity herself and Celestia). But Rarity intends to use it to gradually teach them empathy.
Heroic BSOD: Applejack goes into one upon discovering Zecora has been killed and become a Black Lantern. Worse, since her Ring runs on Will Power, it causes her to lose her powers. She finally snaps out of it to protect Granny Smith from a massive Timber Wolf.
Heroic Sacrifice: Applejack's willingness to do this to save the CMC from falling to their deaths is what attracts the Prime Green Lantern Ring to her.
Cadence almost does this to protect a group of refugees from Black Lanterns using her love to make herself a beacon. Thankfully, Fluttershy and her Star Sapphires show up to help her.
He's Back: Applejack finally snaps out of her Heroic BSOD and creates a massive wall ten pony paces thick, 40 paces high and 100 paces wide to protect Granny Smith from a giant Timber Wolf.
Kaiju: Twilight starts recruiting these into her Corps, giving them sentience in the process. Fluttershy eventually recruits an Ursa Major.
Jumped at the Call: Raindrops refuses becoming the other Lantern groups for various reasons, but devotes herself to becoming a Green Lantern. She ultimately becomes the first person Applejack intentionally recruits.
Mood-Swinger: Applebloom becomes this after the Black Lantern attack on Sweet Apple Acres and discovering Zecora was killed.
Mundane Utility: Some of the Lanterns use their rings for more mundane tasks, like farm work.
My Greatest Failure: Not checking on Zecora, resulting in the Black Lanterns killing her and turning her into one of their own is this to the Mane Cast, especially Applejack who's the one who discovered it and goes into a Heroic BSOD.
Painting the Medium: Whenever one of the rings speaks, it's bolded, surrounded by parentheses, and italicized, like so: ( = Text. = ).
Black Lantern speech has capital and lowercase letters arranged seemingly randomly in the words. Their ring text, besides that and brackets instead of parentheses surrounding the text, is the same as the other ring text.
"Rashomon"-Style: Invoked by Twilight when considering the various view points between the different Lantern Groups they get from their Rings. She has no intention of following in Sinestro's footsteps, but still reads his version of events, as well as wants to hear both the Red and Green Lanterns' perspectives, so she can piece together the truth from their narratives.
Redeeming Replacement: Since they're the Bearers for the most part, some of the new leaders of the various Lantern Corps are this compared to the originals. Most notably is Twilight Sparkle becomes the new leader of the Yellow Lantern Corp, and is still her kind, goodhearted self and even removes Sinestro's name from their Oath. The new Star Sapphires (under Fluttershy) probably qualify as well.
The Red Lanterns are also a bit nicer, in part due to being led by Rainbow Dash, who retains her Undying Loyalty towards her friends.
There's also Applebloom, who despite getting the orange light, learns that it's not a light of greed but of desire. Which manifested from her desire to keep those precious to her safe.
Remembered I Could Fly: In the original Blackest Night, most of the Black Lanterns didn't get much mileage out of their ring abilities (save those who were Lanterns in life), with those who were heroes apparently preferring their original abilities, and the rank and file Blacks being little more than Cannon Fodder. Here, they use their powers far more often.