I would just like to back up what apathy has stated as it answers the question. Some people might be a bit confused by the terminology.
Now of course if you place some lithium in water, it will not have as violent a reaction as sodium which will be less than potassium and so on to cesium having an extremely violent reaction in water. This is due to that electron being "ripped off" of off the cesium. That being so because cesium has the lowest first ionization energy, making it the easiest to lose that electron.
Lithium on the other hand is the strongest reducer (as far as elements go). That is why it is topping those reduction potential lists. If you want an extremely strong reducing agent, then you go to LiAlH4 - and there is your lithium.
And so because lithium is a stronger reducing agent than potassium, a reaction such as Li + KNO3 --> LiNO3 + K (as shown in the experiment done by David Hahn) will in fact work.
I hope this has helped a bit to explain.