You are asking two very different questions, because Adobe Photoshop Lightroom and Adobe Photoshop of course do not have the same system requirements or use the same system resources.

Adobe Photoshop Lightroom 4

Graphics Card:

Lightroom does not currently utilize the GPU for performance improvements. It is outlined in the Lightroom documentation here.

Lightroom requires a video card that can run the monitor at its native resolution. Built-in, default cards that ship with most desktop or laptop systems typically suffice for Lightroom.

Processor:

From Adobe:

The minimum system requirements to run Lightroom are just that: the minimum you need for Lightroom to operate. Additional RAM and a faster processor, in particular, can yield significant performance benefits.

Adobe Photoshop CS6

Graphics Card:

Photoshop CS6 does utilize the graphics processing unit for enhanced performance. Here is some detail from Adobe staff:

Some features require a compatible video card to work; if the video card or its driver is defective or unsupported, those features will not work at all. Other features use the video card for acceleration and if the card or driver is defective those features will run more slowly.

Additional info here.

Processor:

From Adobe:

Photoshop CS5 and CS6 require a multicore Intel processor (Mac OS) or a 2 GHz or faster processor (Windows). Photoshop generally runs faster with more processor cores, although some features take greater advantage of the additional cores than others.

Recommendation

If you have already maxed out your RAM and storage options, I would then decide which program speed and efficiency are more important to you. For example if you are a much heavier user of Lightroom, I would choose processor over GPU. If you are much heavier user of Photoshop, it is a harder decision, and really gets into the specific processor model and GPU model(which I won't go into here, and would be better suited for superuser.com). If it is a desktop model, I personally would go with the CPU over GPU since it is likely you can upgrade the GPU anyways.

To answer your secondary question, if you are using an older version of Photoshop that does not have heavy requirements on the GPU, you still need a graphics card to handle things like Windows and the actual display on your monitor, it just won't be used by Photoshop to offload the heavy tasks it does with many new features.

Additional information can be found in other questions already on this site:

• What laptop specs are important for intensive image editing work?
• What should I consider for buying a photo editing computer?
• https://photo.stackexchange.com/questions/tagged/monitors