I recently picked up a 2001 model bike with non-functioning RSX STI levers. The bike was purchased and ridden no more than 2 or 3 times and put away...for 8 years. Both levers didnt shift up or down.
Sticky STI's, no problem, flush and lub. Nope, not happening. Knowing that the problem was hardend/sticky grease I thought of ways to soften it up. Heat!!!! Ok, so I removed a lever and ran it under blistering hot tap water for a few minutes.
Presto. It worked like a charm!!!! The heat softened up the old lub and allowed the Tri-Flow I lubed it with to work into the bits.
So...onto lever #2 and not wanting to remove it from the bike. Hmmmm....will a hair dryer work?
Presto #2!!! Within 2 minutes of blasting the lever with the hottest heat it freed right up.
If your levers are full of road debris etc. this technique probably wont work as the debris will need to be flushed out. But if you have a STI's that haven't been used much and are sluggish/will not shift try heating them up.