You might want to send Adobe a feature request to allow Grayscale tagged images to be exported to single channel TIF files.
In the meantime have you tried exporting with ZIP compression? Or for maximum space savings to the DNG format?
As a test I created the following files from a Canon 20D raw image:
RGB TIF, 16-bit, ZIP compression (export from Lr) -- 15Mb
Grayscale TIF, 16-bit, ZIP compression (saved from Ps) -- 12 MB
DNG, ZIP compression (export from Lr) -- 9 MB
The full RGB file is not three times the Grayscale and DNG is smallest.