This word is easy to break down; indeed, when you break down many other words, this is part of what you get. It comes from Greek λύσις lusis (noun) ‘loosening, parting’ and refers to breakdown, dissolution, degeneration. Thus we get Lysol, which was originally an oil that dissolves or breaks down things: a solution of coal tar oil in soap.
By itsef lysis is pronounced “lie-sis,” but at as soon as you put it at the end of a longer word, it gets compacted: the usual habit with Greek-derived words is to put the stress on the antepenult (the third-last syllable), so you get electrolysis, glycolysis, autolysis, et cetera, all with the lysis as [ləsɪs] or [lɨsɪs]. And of course the same goes for catalysis, dialysis, and the best-known of the bunch, analysis.
Now, the next thing you’re probably wondering is, “If lysis means ‘break down’, does analysis mean ‘busting your ass’?” Ah, well, it’s not really anal + lysis; the first part is ana, meaning ‘back, again’ – so analysis is breaking something back down. Possibly your resistance, or your patience, self-respect, or fortitude, depending on where and when the analysis is being done and by whom. It could involve busting your ass. But it still doesn’t come from that.
Likewise, dialysis does not mean destroying clocks, soap, or other dial things. And catalysis will not lead to a reduction in the number of available lives for a given cat. Or, well, it may, depending on what is being catalyzed (note the z spelling in the verb, here as in some others; the Brits have generally kept it at s throughout, but oh the Americans and their z’s), but not for etymological reasons. Those would be what linguists call reanalysis… a kind of double-back breakdown. In the search for a solution, the sense is dissolved.
One thing that can be broken down is bellicosity – and armies in general. Take the word for ‘army’, στρατός stratos (as seen in such words as strategy – but not stratosphere, which comes from Latin stratus ‘layer’), put it together with lysis, make it a feminine Greek name, and you have Λυσιστράτη, Romanized as Lysistrata: the Aristophanic heroine who organized women to end the war by withholding sex. The plot of the play does not bear up well under analysis, but it’s a comedy, for heaven’s sake. And anyway, never mind the play: the name of the heroine hasn’t borne up well either. It was pronounced in Classical Greek something like “loo-see-stra-tee,” but it has managed to have the vowels shifted – and, in a fortunately now out-of-fashion version of the pronunciation, even to have the stress altered to match a Procrustean antepenultimate stress: “lie-sis-tra-ta.” Yeccch. Which just goes to show that you can destroy something not only without breaking it down but in fact because you haven’t broken it down.