Both can be used to describe the weather phenomenon (sharing the same kanji), but the more common pronunciation nowadays is "kaminari". "Ikazuchi" was the historical 'pronunciation'* in Heian-era Japan and earlier, so it's less commonly used now except for literary effect (including naming ships). Think of it like using thundre/thonder/thunnere/thonre/thonder/þunre instead of thunder.
(*Well, more like different words with different etymologies that got tacked with the same Sino-Japanese character later on, due to their similar meanings.)
Of course, since it's Ikazuchi, she might be saying her namesake regardless. This comic is, after all, a parody of her intro line.
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