c# - Using input parameter of lambda expression in if statement

Switch from Any to FirstOrDefault, that will return the item that matched the test or null if no item was matched.

var found = myList.FirstOrDefault(x => s.Contains(x));
if (found != null)
{
//some code here
}

If null could be considered a "valid value" for a element in myList you can create a extension method TryFirst

public static class ExtensionMethods
{
    public static bool TryFirst<T>(this IEnumerable<T> @this, Func<T, bool> predicate, out T result)
    {
        foreach (var item in @this)
        {
            if (predicate(item))
            {
                result = item;
                return true;
            }
        }
        result = default(T);
        return false;
    }
}

This would let you do

string foundString;
var wasFound = myList.TryFirst(x => s.Contains(x), out foundString);
if (wasFound)
{
//some code here
}

and tell the difference between a null in your list and a default result.

The above two methods only act on the first item on the list that the Contains will match, if you want to act on all the items use a Where( clause and a foreach

foreach(var item in myList.Where(x => s.Contains(x))
{
//some code here
}

You must promise you will not use the following code and use one of the other options first

You can also do your stated question, it is possible to get a variable assigned to inside lambada. However this can not be done with expression lambadas, only with statement lambadas.

string matachedString = null;
if (myList.Any(x => { var found = s.Contains(x);
                      if(found)
                          matachedString = x;
                      return found;
                     });
{
//some code here
}

But only do this option as a last resort, use one of the more appropriate methods like FirstOrDefaut or write a custom method like TryFirst first.