Why is it that when I import TIFF files into AutoCAD LT sometimes I can change the color of the file and sometimes I can't?  I download a set of drawings from a website for my projects & every once in a while I can't change the drawing to a lighter color so that the line work I'm adding stands out more.  I'm importing the files into paperspace if that makes any difference.

Only bitonal ("black-and-white") raster files can be re-colored to another color using AutoCAD entity properties (Color, Layer, Block, etc.). You will need Raster Design or an external raster image editor to change colors in color raster files (paletted or true-color).

These files are black and white. I place them on a layer with a light gray color so my line work is darker when I print it.  So you're saying I need to convert these files in some way?

Yes, but it is important the TIFF file are "black-and-white" internally (technically, 1-bit color depth in the file) not just visually. Only in this case you will be able to re-color them. You can convert raster files between different color depths with any raster image editor or viewer (Photoshop, CorelPaint, IrfanView....).

I’ve played around with converting tiff files to make them 2
bit color.  It does allow me to change the
imported tiff to the color of that layer. 
However, when converting the tiff I lose a lot of the line work on the sheet.  The Plan sheets I’m working with show
existing features in a lighter gray color (proposed features are in black).  When I convert the tiff I can’t see any of the
existing features because they are too light or non-existent at that
point.  Is there any solution in between?

Depending on the scope of the job and on the abilities of your raster editor, it might be possible to convert your color TIFF file to a paletted image (2 colors + background) and then split it into two monochrome (1-bit) TIFF files - with the black and light-gray "layers". You can then overlay both TIFF files and color them accordingly. They will remain transparent.

Thank you for your comments.   I think I found a work-a-round.  I installed the .tiff file plotter into
AutoCAD LT.  Then printed each page from
CAD & it created a tiff file that I imported back into CAD; these .tiff
files were able to adjust the color by the layer and so on.  Quite a few steps to take on but the end
result was what I needed.  Thanks all!