Check if list<t> contains any of another list

You could use a nested Any() for this check which is available on any Enumerable:

bool hasMatch = myStrings.Any(x => parameters.Any(y => y.source == x));

Faster performing on larger collections would be to project parameters to source and then use Intersect which internally uses a HashSet<T> so instead of O(n^2) for the first approach (the equivalent of two nested loops) you can do the check in O(n) :

bool hasMatch = parameters.Select(x => x.source)
                          .Intersect(myStrings)
                          .Any(); 

Also as a side comment you should capitalize your class names and property names to conform with the C# style guidelines.

Here is a sample to find if there are match elements in another list

List<int> nums1 = new List<int> { 2, 4, 6, 8, 10 };
List<int> nums2 = new List<int> { 1, 3, 6, 9, 12};

if (nums1.Any(x => nums2.Any(y => y == x)))
{
    Console.WriteLine("There are equal elements");
}
else
{
    Console.WriteLine("No Match Found!");
}

If both the list are too big and when we use lamda expression then it will take a long time to fetch . Better to use linq in this case to fetch parameters list:

var items = (from x in parameters
                join y in myStrings on x.Source equals y
                select x)
            .ToList();