厉害 and 利害 are a pair of words which are very confusing since they share the same pronunciation and the same use.
厉害 and 利害 have the same use
The same use of 厉害 and 利害: terrible; formidable; In this case, they are both pronounced lì hai（neutral tone）
两天来我一直头痛得厉害。I have had a terrible headache for the last two days.
This is a formidable move.
He is so nearsighted that he can just see the things put before his eyes. 他的眼睛近视得利害, 放到眼底下才看得清。
靠近地面的风带走砂土最多，因此大块岩石下部磨蚀得最为厉害。kào jìn dì miàn de fēng dài zǒu shā tǔ zuì duō , yīn cǐ dà kuài yán shí xià bù mó shí de zuì wéi lì hài 。The wind near the ground carries most sand with it and so wears the lower parts of big masses of rock most.
眼下，箱子已不完全是黑色的了。它的一边破裂得厉害，露出了木头的本色。 yǎn xià , xiāng zǐ yǐ bù wán quán shì hēi sè de le 。 tā de yì biān pò liè de lì hài , lù chū le mù tóu de běn sè 。By now the box was no longer completely black but splintered badly along one side to show the original wood color.
利害 is different from 厉害
利害 has another meaning with the pronunciation lì hài: advantages and disadvantages; gains and losses; interest
判断往往因利害关系而有偏差。The judgement is often biased by interest.
相互的利害关系把我们联系在一起。Mutual interests tied us together.
此刻的利害关系远远大于一个国家或另一个国家的贸易在世界追求竞争优势。 cǐ kè de lì hài guān xì yuǎn yuǎn dà yú yī gè guó jiā huò lìng yī gè guó jiā de mào yì zài shì jiè zhuī qiú jìng zhēng yōu shì 。The stakes of the moment are far greater than one country or another’s quest for a competitive advantage in world trade.
如果发生一场严重危机，得将其利害关系充分告知民众。 rú guǒ fā shēng yī chǎng yán zhòng wēi jī , de jiāng qí lì hài guān xì chōng fèn gào zhī mín zhòng 。If a serious crisis should arise, the public would have to be informed of its full implications.