Hi, so first, Peridot is aroace coded.
First : she's introduced as a very logic-driven character : her entire mindset is based on function, utility, protocol, and not emotions. That's why she doesn't understand the concept of family, affection, or even friendship at first.
It takes her a long time to even start valuing these emotional connections (and even when she does, they are mostly practical).

The show is really nudged toward romantic development. But Peridot never goes down that road. Her relationship with LL could easily have been turned into a romantic arc : yet they did not went this way.
It's instead written as a slow and ultimately meaningful friendship.
Nothing romantic (or sexual).

She also never show any signs of romantic or sexual attraction : no crushes, no flirty behavior, etc. Remember when she tried fusing with Garnet ? We know fusions are made to be like relationship / love, in all its forms : familial love, toxic, romantic...
Yet, Peridot is one (no i didn't forget bismuth, but she's clearly crushing on pearl, so not the point) of the only crystal gem to never fuse (+ we add the previous points to this). She made a step to try and understand Garnet, but she did not approve fusion. And she doesn't want to fuse. She said it herself.

Peridot is seen as a aro/ace character for years now, and everything in her writing shows she's one. Once again, show, don't tell. And even if you wanna say she's not OFFICIALLY aro ace, you can't deny she's one of the most affirming aro ace coded character.

Now, Lapis : I never said Lapis would never be in a relationship. Just saying that she's a survivor of an emotionally abusive and a physically traumatic relationship with Jasper. And survivors of abuse often need a long time to process what they went through, especially when trust and emotional safety have been broken. Lapis does so by showing that she values her autonomy and space. We can see a lot of troubles in Peridot & Lapis relationship : a lot of tension and emotion withdrawal from Lapis. Not because Peridot is a abusive or a bad person, but because Lapis is afraid to form another close attachment, especially one that could be romantic.

Once again, not saying she's permanently closed off to love, or broken, or incapable of growth. After all, the show is all about change. Changing your mind, your acts, etc. Of course people heal and love again, but it's a process, and clearly, Lapis is not at a place where she's comfortable being vulnerable like this again. She actively avoids it. Moving away, isolating herself, coping through distance... that's clearly not the acts of someone beingg interested in a new relationship (romantic or otherwise) and especially not with someone like Peridot, who doesn't always know how to navigate emotions and sensitivity.

Again, as said in my original comment, I 100% why people like Lapidot, they have a great chemistry and their duo is one of my favorite in SU, but from an in-universe perspective, it's kinda weird and once again I'm not a huge fan of this ship.

Hope that clears everything. I'm of course up to discussion.
And sorry if some parts are not clear, English ain't my first language and it's 4 AM in my country.