Tomb Raider on Low Specs

Put it on Ultra, be sure to turn ON TressFX, you will get a barbecue with your PC :D But seriously it should work on medium if you turn off all anti aliasing, FXAA, or other postprocessing things and Vertical Sync.

Best bet is to lower shadows to a minimum, then fiddle around with the rest options until you're comfortable with how it looks and runs

In my experiences in the past. Turn off any and all anti aliasing. AA, AXAA whatever ones they have. Turn the shadows down a bit too, experiment with those. Turn off the physix. Turn off the fancy hair.)

Experiment ? It's not like it requires you to change the settings in a launcher before you run it, you can see live if any change is an improvement expecially if you have an FPS overlay...

It should work with:
medium/high textures
medium shadows
anti aliasing off
vsync off
and 720p resolution
I played it that way a year ago when I was still running a GT9600 so you should be fine.
Maybe you can also put the resolution higher than 720p, just try how it runs.

well if my even LOWER spec PC could run it at decent 30-40 fps, sure your thing can run it on medium.
AMD Phenom II x4 3.0Ghz
4Gb RAM
AMD Radeon HD 5670 512Mb

i was running it on 1600x900 resolution, medium textures, lowm sahdows... not remember all the settings but it hink i lower the draw distance too.

should be fine - I was running it in high with:

i5 650 (@3.4 GHz)
HD6850 1GB
12GB RAM

Also buy some RAM - getting 8GB should be ultra cheap nowadays, and having 4 GB you're basically just hurting yourself ;p

You should be able to play it with high textures, depends on your screen resolution though.