Why is aconitase classified as a lyase?
The mechanism of aconitase classifies it as a lyase, even if (under most physiological conditions), the relative concentrations of substrates results in it catalysing the conversion of citrate to isocitrate. In short, it is not an isomerase because the substrate is released after each step.



As the mechanism of aconitase shows, it catalyses the conversion of either citrate or isocitrate to aconitate as well as the reverse reaction. This is similar to the reaction catalysed by fumarase, which is the reversible addition or removal of water. 



Because the physiological concentrations of citrate is much larger than the concentration of isocitrate, aconitate overall catalyses the reaction from citrate to isocitrate, and does so via catalysing two lyase reactions. 

Regarding the other part of your question, hydrolases are a completely different group of enzymes, and none of the reactions involved are related to hydrolases in any way. 

While water is in fact involved in the reaction, it is not used in the process of hydrolysis. To be specific, hydrolysis (in its enzymatic/organic, and not chemical sense) requires that water be a substrate required to break apart a molecule A-B into A and B. Since the addition of water does not result in citrate/isocitrate being broken down into two smaller organic molecules, aconitase is not a hydrolase.