"Can you burn a file and have that file locked to the CD so no one can then make a copy of the file on the CD?"
If your goal is to send someone a CD and give them access to the files on it, there is not a good way to lock a CD from being copied by the recipient. Hollywood has tried unsuccessfully to prevent copying of their materials and most of us don't have their budget for copy protection. On the other hand, if you are creating a file archive, you can encrypt the contents of the disk so that a password is required to access them.
The problem with trying to copy-protect CD contents is that as soon as you make them accessible to someone, the contents of a CD are reasonably easy to copy. You can reduce the usefulness of a CDs contents, making it less desirable to copy, but actually preventing copying is fairly difficult.
For instance, if you want to share some photos with someone on CD, but you don't want them to simply take the photos and print them out, you could embed the photos in an .exe file or embed them in a Flash movie. While both of those options can be decompiled to remove the contents, the average person won't take the time to do it, so you gain some level of file protection by simply making it inconvenient. The trade off in this type of scenario, is you will make it more difficult to view the files, which can increase your own support headaches.
For text documents, using a PDF file that sets permissions, like preventing copying and printing, can be a way to lock down the contents of the document. Here again, you can reduce the likelihood of copying, although you aren't really preventing copying as it is fairly easy to find resources to extract the contents of a PDF.
Encrypting CD Contents
If you want to simply encrypt the contents of a CD, so they aren't viewable without the encyption key, you can use something like TrueCrypt to create an encrypted file container on a CD-RW and then copy the files you want to into the volume.
When the volume is not mounted through TrueCrypt, the actual files will be completely inaccessible.