A completely delusional drunk, General Ivolgin is the embarrassing, unacceptable dad of Ganya, Varya, and Kolya, who ends up suffering a stroke in the middle of the street after a foiled attempt to steal money from Lebedev.
On the other hand, we could come up with another way of thinking about Lebedev—but only in combination with the character of General Ivolgin. Think back to all those Shakespeare plays you've read and seen performed. Remember how no matter how totally bleak and depressing the main action, there is always some kind of comic relief going on. Perhaps the same thing is going on here, with General Ivolgin being this novel's answer to that drunken old porter in Macbeth who talks about how liquor "provokes the desire but takes away the performance." (It's a dirty joke, kids. Have someone older explain it to you if you don't know what he's talking about.)
And yes, it's kind of sad that this man who somehow rose to the rank of general in the army is now a rambling alcoholic, but taken by themselves those rants are so over-the-top that they are just sublime. The building of lie upon lie upon lie, and the slight adjustments Ivolgin makes whenever someone questions the wildly conflicting logic in his tales of derring-do, are a kind of spoken-word performance art, no?
Of course, the highlight, the grand opus, the master display in world-class lying is that four page story that Ivolgin tells Myshkin all about how he was a page in Napoleon's service during the War of 1812. Amazing stuff. Even more amazing? The large and loud Ivolgin in combination with the cringing, slouching, scraping Lebedev, who nonetheless manages to get the upper hand when he refuses to acknowledge the return of his stolen wallet and thus drives Ivolgin so crazy that the general has a stroke.