I have a manual lens Samyang 14mm F2.8 IF ED UMC AE Aspherical. It has no contacts plate so there is no autofocus support and my Canon has no information about the current focal length and aperture value.
To update the EXIF metadata for images I use ExifTool utility.
exiftool -LensModel='Samyang 14mm F2.8 IF ED UMC AE Aspherical' \
-FocalLength='14.0 mm' \
-FNumber='2.8' \
-if 'not $LensModel' \
-m -overwrite_original \
./IMG_*.CR2
Lens metadata will be updated for each IMG_*.CR2 file in the directory with no "LensModel" tag.
As you see, now there is a lens name, current focal length and aperture value. Lens correction profile will be loaded correctly.
Problem may occur when setting the correct aperture value if you change it while shooting. But in most cases with fixed aperture value, you will be succeeded.