This is a complete list of recurring gags throughout the Shorts, and from Seasons 1, 2, 3 and 4 of the series.
Frequent Running Gags
Lincoln: Breaking the fourth wall to explain what's happening in each episode, coming up with long operation names (sometimes even ending with "and maybe think of a shorter name for this operation"), reading comics in his undies, making up funny nicknames for him and Clyde over the walkie-talkies, and making card puns while playing Ace Savvy.
Lori: Texting/calling Bobby with her phone, farting and denying it, being territorial, or saying "literally".
Leni: Having ditzy moments or making crazy outfits.
Luna: Speaking in a British accent, being asked to play music for a scene, or quoting song titles and lyrics.
Luan: Telling puns and jokes for every situation (which most people find very bad).
Lynn: Always engaging in sports, or rough activities, turning everyday things into a sport, roughhousing with her siblings, and having wacky superstitions.
Lucy: Always appearing suddenly, scaring her siblings, or other people, crushing on Edwin, and saying verbs instead of doing the actions.
Lana: Having gross habits, eating gross things, and being an animal lover.
Lola: Being bratty, performing mean acts towards her siblings, loving glitter, giving people nicknames ending in "-ington", and having tea parties.
Lisa: Talking in technical terms, making a creepy smile, experimenting on people, experiments blowing up in her face, and saying she normally doesn't express emotion before expressing emotion.
Lily: Saying, "Poo-Poo", pooping her diaper, and running around naked.
Clyde: Talking about how beautiful Lori is, and how he wishes to have a date with her, acting like a robot and/or bleeding from his nose when he's around her, breathing into a paper bag when he's scared, passing out, and quoting from Dr. Lopez.
Rita and Lynn Sr.: Not showing their faces. (This gag ended after of Season 1, as their faces were finally revealed in the Season 2 premiere "11 Louds a Leapin'".) In Lynn Sr.'s case prefixing words with "ding-dang" when frustrated, getting scared or teary-eyed easily, and singing while doing chores.
Ronnie Anne: Insulting Lincoln playfully and insisting she's not Lincoln's girlfriend.
Bobby: Being clumsy and acting romantic with Lori.
Although Lincoln speaks to the viewing audience in most episodes, characters in bold have been observed doing so as well while others look at the fourth wall, not speaking to the audience, but breaking the fourth wall nonetheless.
Left in the Dark: Operation Distract My Sisters So That I Can Get to the TV First and Watch the Special Live Season Finale of ARGGH and Think of a Shorter Name For This Operation.
Come Sale Away: Operation Pretend You've Never Met Me And Are Really Interested In My Stuff So Other People Will Buy It And Also Think Of A Shorter Name For This Operation.
Homespun: Operation Paint The Peeling House To Give Mom And Dad The Greatest Anniversary Gift Ever And Also Think Of A Shorter Name For This Operation.
Season 2
11 Louds a Leapin': Operation Scale the Fence and Retrieve Big Red Before Mr. Grouse Finds It and Takes It Into His House Forever and Also Think of a Shorter Name For This Operation.
The Whole Picture: Recreate All My Most Cherished Memories & Think Of A Shorter List Title, List.
Operation Sneak Into a Yearbook Group Photo So We're Not Forgotten Like Marty What's-His-Face.
Operation Get Coach To Hire Us So We Can Edit Ourselves Into The Yearbook Photos.
Fool's Paradise: Operation Find Our Family and Get Back at Luan for Causing Years of Emotional Damage and Also Think of a Shorter Name for This Operation. (Lynn Sr. made this long operation name, not Lincoln.)
Health Kicked: Operation Get Mom and Dad Out Of The House and Into Shape.
Season 3
Breaking Dad: Operation Remind You I'm Your Daddy and That Guy Next Door is Just an Old Coot With a Bad Lasagna Addiction. (Lynn Sr. made this long operation name, not Lincoln.)
Other media
Promotional video for Lost Control: Operation Track Down Which Of My Sisters Has The Remote So I Can Watch My Favorite Show And Think Of A Shorter Name For This Operation.
Kids' Choice Awards 2017 Instagram post: Operation Let's Win a Kids' Choice Award for Favorite Cartoon While Keeping Slime Out of My Hair and Also Think of a Shorter Name For This Operation.
Get Out of Project Day Without Making Everyone Mad Operation.
Divert and Distract Escape Operation.
Fool My Sisters and Then Walk Merrily Away Operation.
Operation Be First in Line to Play Marshmallow Martian Blasters and Get the High Score.
Help With Project Day Without Actually Helping Operation.
Be Really Eager but Absolutely Useless So No One Will Want My Help and I Can Sneak Away Without Anyone Knowing What I'm Really Up To Operation.
Operation Convince My Sisters I'm Ready for the Responsibility.
Operation Float Through Project Day Being Utterly Useless So No One Will Miss Me and Get to the Arcade First and Also Think of a Shorter Name for This Operation.