The problem is that if I enable lazy loading for the widget, I can’t see the reviews in the Google search console. And consequently, Google can’t see the reviews’ snippets in search.
I turn off lazy loading, and everything is fine. The review snippet shows up in Google search, google also sees the reviews. However, this is very, very bad for page speed.
Hi there @Maksim_Kim and welcome to the Community!
That’s true that the lazy loading feature prevents Schema Markup from working. I am so sorry about it!
Please let me talk to our devs and check if anything can be done. I’ll get back to you once any news come up 
@Maksim_Kim I’ve talked to our devs and, unfortunately, there is no option to change this behavior now. I am so sorry!
I agree that this functionality is really important. I’ve moved your request to our Wishlist and we’ll try to think it over in our future updates.
I’ll keep you in the loop regarding any changes