Can landscape adhesive be used for a masonry fire pit?

I talked to a sales person at a hardscape place.

He gave me:

Loctite PL 500 landscape

EDIT: I used the PL 500 Landscape adhesive towards the outside and it's solid.

Regarding Loctite PL 500 landscape adhesive (mentioned in the asker's answer)...

Service Temperature: -20°F (-29°C) to 150°F (66°C)

No, landscape adhesive (or at least that specific product) isn't rated for temperatures encountered in a fire pit.

That said, if you put a bead toward the outside of the course rings I'd expect it to hold up fairly well. Temperatures out there may get high enough to soften it, but probably wouldn't burn it.

Of course, there may be landscape adhesives (or products that could serve as such) with higher temperature tolerance.

I would just use a fireplace mortar (like this example from Ace Hardware).

For flatter bricks I have used this furnace cement (sold by Grainger, among others).

I have made a lot of fire pits. I would go with the first one - or any type like that (the link was not a recommendation just example). Note that I have used pavers almost exactly like yours with about the same size pit, maybe a tad bigger. Note that some of them cracked when we made some extremely hot fires involving large oak logs.