Well, for one thing Lightroom and Photoshop are both just "interpreting" Raw data according to built-in algorithms that you then can adjust at will.
Then, when you Export or save an image from Lightroom or Photoshop, you will want to have the image in a color space that is "friendly" for your intended output. This will typically be the sRGB color space, since common Web and image viewers are "dumb" when it comes to such things. So, check your Lightroom Export dialog and you will see a selection for color space -- it could be set to aRGB or ProPhoto RGB, both of which will throw colors off in a generic Web browser. Set it to sRGB and see if it makes a difference. The same with Photoshop -- Camera Raw may be converting to another color space. Check the link at the bottom of the Preview window and see if it says anything other than srGB. And then also in the Photoshop editor, check in your Edit/Color Preferences and ensure that you are set to use sRGB.
Then, there is the subject of color management that you will want to tackle, including monitor calibration -- if you look at the top of the page for this section, you will see a couple "stickies" on color management and color problems that you will want to check out. Photoshop and Lightroom both are designed to use monitor "profiles" that sometimes can get thrown off.