I would definitely get Lightroom to go with Photoshop. I still remember when I started using Lightroom 1.0. The time it took me to process a batch of pictures dropped by about 70%. Of course, that was before Bridge, so ymmv.
Basically, Lightroom streamlines your workflow. You can apply a present of basic processing at the point you import a picture. Then you can quickly go through a set of pictures flagging which ones you want to keep and applying keywords. Then you can step through picture by picture making adjustments very efficiently. It handles lots of basic functionality like cropping, white balance, tone adjustments, color adjustments, dust removal and spot healing, noise reduction, lens corrections, and capture sharpening. You can also make target adjustments such as gradiant or painted adjustments to exposure, contrast, saturation, and sharpness. The best thing is that all of these adjustments are parametric, which is to say that they are all saved as instructions rather than actual changes to the picture. That means that you can have multiple sets of instructions for one picture processing it in different ways (B&W and color versions, different crops, etc).
In my work, I generally only go into Photoshop for a handful of purposes. I use it when I need something special that I can do as well in Lightroom, like extreme noise reduction or adding or removing elements. I also jump into Photoshop when I really want to work on a picture in gory detail.
In summary, I think Lightroom will give you the following benefits:
1) Better organization than Picasa (except the lack of face recognition)
2) More efficient workflow
3) Parametric editing
It will not completely replace Photoshop.