The images should look alike. There is an active thread in Color Management about the problem of images looking different in Lightroom and Photoshop. That might help you (although the Photoshop images look darker) in that thread.
But before you get to that, be sure that you aren't applying some preset upon import to Lightroom that is darkening/saturating the images. Under Presents in the Develop Module, choose "General Zeroed" when you first import an image from Photoshop. Also, check to see what colorspace the image has that you are bringing into Lightroom. As the other space points out, Lightroom uses ProPhoto RGB. That might make a difference.
Try this: Take an image. Don't open it in Photoshop. Import it into Lightroom and use the zeroed preset. then "Edit in Photoshop". Don't do anything to it there either. Just compare how they look on your monitor, side by side at the same time. Strangely on mine, Photoshop image is darker, not lighter as you report.
I'd suggest you follow the discussion in Color Management as it has a number of posts, but no solution so far.