If you don't want to buy the Image module (but who wouldn't

), you can probably roll your own solution pretty easily. TIFF has been an open standard for quite awhile (I wrote a limited reader for it over a decade ago). You can find references to the standards in the
Wikipedia article on TIFF. Reading the header is not difficult, if you understand how to read binary files. Your biggest issue will be reading compressed data. Note that TIFF is a
huge standard. You won't be able to implement all of it, but implementing the part you need should be pretty easy.
However, this is reinventing the wheel. You might try one of the free libraries, such as
ImageMagick, to help there. LabVIEW has shared library and command line interfaces to external programs, so you should be able to do what you want to do.
If you need further help, let us know.