I was asked before which conjugation of 이르다 is correct, 이르러요 or 일러요. The person who asked had seen both of them and wondered whether one conjugation was preferable to another. The answer is that neither is preferable to the other because they’re different words!
이르다 has more than one meaning, and the two conjugations, 이르러요 and 일러요, come from two different meanings that are two different types of irregulars. Let’s take a look.
러 irregular 이르다
Let’s look at 이르러요 first. This one comes from the 이르다 that means “to reach, to arrive (at).” It is part of the 러 irregular group. The group of 러 irregulars is very small (I can’t think of any others off the top of my head at the moment!) and their roots all end with 르. For this group, when adding something like -/어요, the -어 becomes -러 to create 이르러요 instead of 이르어요.
르 irregular 이르다
일러요 comes from the 이르다 that means “to be early,” which is a 르 irregular. That is, when followed by a vowel (such as is the case when conjugating with -아/어요), the ㄹ is doubled and the ㅡ is dropped. Since the preceding vowel is 이, we conjugate it with -어요 and end up with 일러요. Other verbs in the 르 irregular group are 모르다 (몰라요) and 부르다 (불러요).
As always, happy studying!