If you reduce the file size in Photoshop you reduce the pixel dimension of the photo which means that you throw information away - independantly if you save as JPG or as TIFF or PSD.
That means that the reduction in file size is a reduction in image quality.
If you want to print the image you need a certain resolution (dpi) for the print - typically 300 dpi.
If you want to make a print of let's say 8" x 10" at 300 dpi you need a pixel dimension of 2400 x 3000 pixels which results in a file size of roughly 22 MB (flattened file).
If you have reduced your file to 12 MB you cannot make a print of 8 x 10 at 300 dpi without upsampling first, i.e. Photoshop (or Lr) have to "invent" the missing pixels.
So reducing the file size is simply not an option - unless you use your images exclusively for the web where you don't need large file sizes.
If you edit your Raw files in Photoshop you have to live with large file sizes.
The only way to avoid that is: Do edit in Photoshop only if you absolutely cannot do it in Lr.