Building on what "LLC5" says above, there are a number of options for lubricant in the Tremec six-speed manual. What you use depends on your budget and to what duty cycle the car is subjected.
If cost is a concern and the duty cycle is normal driving, the factory specified manual transmission lubricant is ok.
If cost is a lesser concern and normal driving is the cycle, Red Line D4 is an excellent choice.
If cost is lesser concern and the duty cycle is aggressive driving in warm/hot weather, either Red Line MTL or Gibbs Driven STF are both good choices. Each is formulated for high-performance street use and occasional racing.
Is cost is not a concern and the duty cycle is racing, Red Line Superlight Shockproof Gear Lubricant is an excellent choice. It's probably about the highest-performance low-viscosity gear lube you can get. I use it in both my C5 and my C6. There is one slight negative of Red Line SLSP and that's cold shift quality is not so good, but as soon as the lubricant warms just a bit, that issue goes away. It doesn't even need to get to operating temperature. It just needs to get from cold to lukewarm and the shift quality improves greatly. Once the trans is at operating temperature shift feel is better than what you get with D4.
Lastly, let me say that all the high-dollor lubricants on earth will not improve shift feel if either the clutch needs to be bled or the shift linkage is out of adjustment. On a 13 year old car, you may want to check those two items.
