How to “let” in lambda expression?

So, you can use the extension method syntax, which would involve one lambda expression more than you are currently using. There is no let, you just use a multi-line lambda and declare a variable:

var results = Stores.Where(store => 
{
    var averagePrice = store.Sales.Average(s => s.Price);
    return averagePrice > 250 && averagePrice < 500;
});

Note that I changed the average price comparison, because yours would never return any results (more than 500 AND less that 250).

The alternative is

var results = Stores.Select(store => new { Store = store, AveragePrice = store.Sales.Average(s => s.Price})
    .Where(x => x.AveragePrice > 250 && x.AveragePrice < 500)
    .Select(x => x.Store);