Never had this soup myself but I love trying to make a vegan/vegetarian version of existing dishes.

I found this recipe on google: https://girlandthekitchen.com/avgolemono-soup-greek-chicken-soup-lemon/

Swapping the chicken broth for vegetable broth is one option, but I’ve also seen some vegan chicken broth products. We use one that comes in a powder form from a local health food store. There are some on amazon as well.

Something like this: Better Than Bouillon, No Chicken Base, Vegan Certified 8 oz. https://www.amazon.com/dp/B000N7YKQK/ref=cm_sw_r_cp_api_i_bgojDb6Z55B60

You could also make your own vegetable broth. Homemade broth is really tasty.

For the chicken meat, I’ve had good luck with butler soy curls in a soup. They stay together well and don’t turn to mush In a soup like a lot of fake meat products. I usually brown them in a sauté pan first. If you hydrate them in your broth they take on its flavor. They also sell a vegan chicken flavor seasoning for it (same brand) but I’d imagine your broth will give enough flavor on its own but you can experiment.

Butler Soy Curls, 8 oz. Bags (Pack of 3) https://www.amazon.com/dp/B00HAS1SVU/ref=cm_sw_r_cp_api_i_thojDbHX21G1Y

Chik-Style Seasoning - 10.75 oz Jar https://www.amazon.com/dp/B008UYIW8U/ref=cm_sw_r_cp_api_i_1iojDb88KXZ9X

The tricky part is probably the eggs. You’ll have to experiment here to get what you’re after.

It sounds like they’re being used as a thickener and making the soup creamy. The recipe calls for mixing the eggs with lemon juice almost like a mayonnaise or a hollandaise sauce.

A “flax seed egg” might work for you, google it and you can see how that’s made. I’d also consider puréed silken tofu. My mom uses silken tofu instead of egg in her cheesecake recipe with pretty good luck. Some combo of the two might even work.

Not sure if this soup has an eggy flavor from the eggs, but if that’s missing you can use a little black salt which has an eggy flavor.

It might take a few try’s and some experimentation but it looks like it can be done.