This question already has an answer here:
Is there a construct in C# which allows you to create a anonymous class implementing an interface, just like in Java?
As has already been stated, no, this is not possible. However, you can make a class that implements the desired interface and accepts a lambda in it's constructor so that you can turn a lambda into a class that implements the interface. Example:
public class LambdaComparer<T> : IEqualityComparer<T>
{
    private readonly Func<T, T, bool> _lambdaComparer;
    private readonly Func<T, int> _lambdaHash;
    public LambdaComparer(Func<T, T, bool> lambdaComparer) :
        this(lambdaComparer, EqualityComparer<T>.Default.GetHashCode)
    {
    }
    public LambdaComparer(Func<T, T, bool> lambdaComparer,
        Func<T, int> lambdaHash)
    {
        if (lambdaComparer == null)
            throw new ArgumentNullException("lambdaComparer");
        if (lambdaHash == null)
            throw new ArgumentNullException("lambdaHash");
        _lambdaComparer = lambdaComparer;
        _lambdaHash = lambdaHash;
    }
    public bool Equals(T x, T y)
    {
        return _lambdaComparer(x, y);
    }
    public int GetHashCode(T obj)
    {
        return _lambdaHash(obj);
    }
}
Usage (obviously doing nothing helpful, but you get the idea)
var list = new List<string>() { "a", "c", "a", "F", "A" };
list.Distinct(new LambdaComparer<string>((a,b) => a == b));
                    
                                            
No. C# doesn't support anonymous classes (except anonymous types which can't define methods).
No, a Lambda Expression can not implement any additional interfaces than it already does.
You're also comparing the wrong things. I'm guessing you really meant to ask if anonymous types in C# can implement interfaces. The answer to that is also no.