Do you have to delete the file from some other script? Or would it be more reasonable to simply truncate() TEST.NEW from your main script after it aquires the lock?

open STDOUT, ">>$dir/TEST.NEW" or exit 1;
open STDERR, ">>&STDOUT" or exit 2;
flock STDOUT, LOCK_EX | LOCK_NB or exit 3;
truncate STDOUT, 0; # delete everything from the file

# The remainder of the program will be writing to an
# empty file.  

close STDERR;
close STDOUT;
[download]

There is a way to check if the file is locked from another script but you can't safely delete it because as soon as you close the file, so that you can delete it, it will be unlocked and there is a slight chance that some other process will write to it in the interim.
To prevent this from happening, both processes either need to use truncate(), in which case the file doesn't get deleted but you still accomplish the same thing - no data in the file; Or, as the second option, both processes need to use a second file that they would lock whenever they need to update/delete TEST.NEW.

--perlplexer