I stumbled upon 死に至らしめました today and since 死に至る exists, at first I was trying to understand the conjugation but then I saw that jisho consider it as a whole verb or expression. There seems to be a couple of verbs having this suffix like 懲らしめる or 成らしめる. Some are considered archaic and almost none are really considered common. Assuming I didn't miss anything obvious, is this an old form of conjugation?
Since it is a causative, 至らしめる can be written as 至らせる. That said, 死に至らしめる is more like a fixed expression and probably more common than 死に至らせる.
Both 懲らしめる and 成らしめる similarly derived from 懲る (= modern 懲りる) + しめる/成る + しめる. They are recognized almost as independent words (懲らしめる has an entry in デジタル大辞泉; 成らしめる doesn't).