I have quickly read over the Microsoft Lambda Expression documentation.
This kind of example has helped me to understand better, though:
delegate in
The biggest benefit of lambda expressions and anonymous functions is the fact that they allow the client (programmer) of a library/framework to inject functionality by means of code in the given library/framework ( as it is the LINQ, ASP.NET Core and many others ) in a way that the regular methods cannot. However, their strength is not obvious for a single application programmer but to the one that creates libraries that will be later used by others who will want to configure the behaviour of the library code or the one that uses libraries. So the context of effectively using a lambda expression is the usage/creation of a library/framework.
Also since they describe one-time usage code they don't have to be members of a class where that will led to more code complexity. Imagine to have to declare a class with unclear focus every time we wanted to configure the operation of a class object.