Agitato is generally understood to be allegro agitato — allegro plus agitation — unless there is something to indicate otherwise. Allegro is generally around 3 times as fast as lento (~144 versus ~50 bpm), so you can get an idea of the tempo change from that. It's quite significant.
(So in one sense, I disagree with Mark; the house on fire with the baby upstairs would warrant prestissimo agitato.)
As you've noted, you can also check out recordings / performances to get an idea, such as this one (the tempo change occurs at 1:45):
Amazingly, I found a great answer on Yahoo Answers (of all places). It notes that these terms had a common interpretation that one would just pick up, rather than a set definition. The usual speed for allegro agitato would be about the same as allegro moderato, to which to add "the element of agitation".
The most relevant excerpt:
"A tempo agitato" derives its understanding directly from 'a tempo ordinario' -- the point being that the understanding of the semantics of the overall detail in notation defines and decrees what 'ordinario' amounts to in ticks of the clock, this being the judgement the performer is assumed to know how to make -- which means that the style and metric detail of the notation for a work only marked 'Agitato' is the key to setting the precise clock for the notional 'Allegro moderato' the implied (a tempo) prefacing the solitary Agitato is meant to stand for.