LevXis's biggest rival is YipXis.All four ships are possible (Although LevXis
and YipXis have the highest chance of sailing) for Alexis mentioned to Aphmau in Puppy Love | Minecraft Diaries [S2: Ep.12 Minecraft Roleplay] where she mentioned she had a crush on Levin, Kyle, and Malachi. She didn't mention liking Yip perhaps indicating they are nothing more than best friends. But who knows?
Many people say LevXis is like Garmau over again. Which is sort of true. Although instead of Levin being like Garroth (Although said otherwise by looks), he is like Aphmau. Alexis instead of being Aphmau (Although said otherwise by gender), is like Garroth. (Well Season 2 Levin and Alexis to Season 1 Aphmau and Garroth)
Not much is known about they're relationship aside that Levin is Alexis's Lord and Alexis is Levin's Guard. (*Cough* Garmau *Cough*) It is theorized that Levin had a crush on Alexis somewhere in the 15 year time skip. Alexis had a crush on him, along with Malachi and Kyle, in the 15 year time skip. But now she has settled with only one, or has chosen someone else. (Yip)
Levin, like Aphmau, is a lord and hasn't really thought about love, which was indicated in A Phoenix Drop Wedding | Minecraft Diaries [S2: Ep.51 Minecraft Roleplay] When Aphmau asked Levin when he thought he would get married, Levin said he almost had a heart-attack after Aphmau said she was teasing him. He said he didn't have a girlfriend YET, which Aphmau teased that Levin had a crush on someone. Levin denied it though.
Alexis, like Garroth and Laurance, is Levin's guard. In Puppy Love | Minecraft Diaries [S2: Ep.12 Minecraft Roleplay], Alexis mentions that she had a crush on LEVIN, Kyle, and Malachi.
There is only one moment we KNOW/have seen. Which is this one:
The Tossed Cats | Minecraft Diaries [S1: Ep.88 Roleplay Adventure]
Aphmau was checking on Levin and the other kids. When Aphmau was checking on Levin, Levin, despite being only 1 or 2 years old, said:
"Alexis is pretty!" Aphmau admittedly told Levin to chill out, saying he was too young for 'pretty' stuff.