To do exactly as you say you would need a RandomAccessFile - see API docs
there are readLine() and writeBytes(String) methods, so you would seek
forward x lines readLine and then seek back x lines to writeBytes, where x
is the number of lines you wish to skip and you would need to know the
length of these lines, because you know or by seeking 1 char at a time and
testing for line terminator.
So obviously this is a pain and proably slow, coupled with the fact that
properly buffered serial access is *very* fast, I'd just read from one file
then write it out to another.

new BufferedReader(new FileReader("mySourceFile.txt"));
new BufferedWriter(new FileWriter("myOutFile.txt"));
When you're done rename the file.