You shouldn't be working with huge strings at all.
If this represents a file's content, read it using File.ReadAllLines() and take the array's Length.
Otherwise, count the lines while you collect the data, not afterwards.
Dealing with a huge string isn't doing the caches any favors.
And if you can't avoid it, I would consider:
static long LinesCount(string s) {return s.Length-s.Replace("\n","").Length;}
which was in one of my very first CP posts, a couple of years ago.
:)
I am an engineer with a background in electronics, software and mathematics.
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