The pronunciation of 吏 (lì) is frustratingly hard to remember since it's different to two similar-looking characters 史 (shǐ) and 使 (shǐ). Sometimes learning the etymology, and the reason why a character is pronounced a certain way, can make it easier to remember how to pronounce. Googling gave me this, but I didn't immediately find anything about pronunciation.
Question: Why is 吏 (lì) pronounced differently to 史 (shǐ) and 使 (shǐ)?
Let us look at the reconstructions (specifically, at Baxter-Sagart):
I will append also the probably basic etymon, even though it is written with an unrelated character:
The relation between all the words is clear:
we have a basic root rəʔ 'to serve' (which, per Schuessler, is the same as 理 'to regulate, to administer'; Baxter-Sagart p. 144),
from which we get 吏 'officer' rəʔ-s with the ordinary nominalizing suffix -s,
with the valency-increasing prefix s- we move to 使 'to send, to cause' s-rəʔ,
and finally nominalize the latter as 使 'envoy' s-rəʔ-s ('one who is sent').
(The verbal meaning for 使 'to be sent as an envoy' s-rəʔ-s seems to be a later development when the Old Chinese morphology alrealy broke up at it became possible to just fluidly change parts of speech, per Schuessler p. 350; same for 史 'scribe' s-rəʔ, which looks like a direct change of parts of speech from 使 'to send, to cause, to employ' s-rəʔ).
From these on, the current pronunciations are all directly derivable. Thus, 吏 actually maintains the original consonant the best of all; all the rest in the group use the valency-inclreasing s- prefix and thus obtain the initial s-r- cluster, which is quite expectedly simplified to a retroflex version of [s], that is, [ʂ].
I'm entirely unqualified to talk about phonology, but from I can tell, 吏, 史 and 事 all evolved from the same character, thus probably share the similar pronounciation in ancient times. 吏's entirely different pronounciation is likely a result of 训读, where the pronouciation and the glyph of a character mismatch. Nowadays 训读 usually refers to this phenonmenon in Japanese, but it did happen in Chinese as well. Also see 文白异读（Literary and colloquial readings）
Words that look similar do not always share the same origin or phonic element.
e.g.
人 and 入; 全 and 金; 赤 and 亦
木，林， and 森 all sound different from each other
Sometimes, two different parts from two different characters would evolve into the same form
