You have a couple of options.
One option is to make the String LB variable a static public variable of your first class, or private with a getter method to retrieve it.
The second option depends on how the first class creates an instance of your second. You could make a constructor that accepts a string value, which you would pass in when creating the object to call the sql.
I guess it depends on how you have you program setup. I have something like this in a swing program I wrote. I store the sql string in a public static String variable of my gui java class. Then when I need to execute the sql, I create an instance of the second class, then call it's sql method that takes a String parameter as input, which is where I pass my String value in to execute.
For example.
Class one has public static String mySql;
Class two has a method named executeSql(String sql);
After I create some sql in a string in Class one, I create an instance of Class two and call classTwo.executeSql(mySql);