Hello! I have Meyer lemons in large pots and was wondering if it was possible to have companion plants in the same pot (like mint or certain perennials) that would help in avoiding pests and enhancing the soil. Can they coexist in the same soil or should I just put smaller pots with companion plants inside the bigger pot surrounding the tree?

I vote, use other pots. For one thing, I don't think other plants will take well in the established roots of the lemons.
Mint, if happy, is very aggressive, as you may know.

I do think it can be pretty having other plants potted to fill some of that empty space. And they may even shade the pot a little.
And, I don't beleive in companion plants being very effective at pest control or enhancing the soil in a pot.
Let's see what others say

I plant a lot of small ornamental groundcovers in my pots. Sedums, crassulas, sedges and grasses, things like that. Proportional to the pot and plant.

Digging holes to plant something, perennials with deep roots, anything you want to pull later... Citrus roots are shallow - damaging them will cause the tree to lose vigor. I don't think companion plants deter pests but will use nutrients and moisture from the soil meant for the citrus tree. Adding pots to the top of the soil would be like adding more soil - the roots will surface under the pots.