Q:

string1 >= string2 not implemented in Linq to SQL, any workaround? 

How do I do string1 >= string2 in Linq to SQL? 

A:

If you're looking for => which would normally be written as >= then you cannot do this directly with strings.   You can get the same behaviour via CompareTo:
string1.CompareTo(string2) >= 0

In this case, the result being less than or equal to zero means that string1 would be sorted before string2 and therefore is greater. 
FYI the => operator in C# is only used in the definition of lambda expressions. 

A:

string1 >= string2 is not supported in C# Linq To Sql.   The String class does not override the >= operator at all.   It only overrides the ! = and == operators.  You can verify this by trying to compile the following method
public static void Example() {
  int val = "foo" >= "bar";
}

If you want to compare to Strings in LinqToSql you should be able to use the static String. Compare(string,string) method. 