Hola Nu

You can use both "lo" and "le" for "him". Escuchar is a transitive verb, as in you listen to something or someone, that something or someone being a direct object (or direct object pronoun) - so, following this, you should use "lo" (for it masculine or for him) and "la" (for it feminine or for her). However, there is something called "leísmo" in Spanish, which is using le instead of lo as a direct object pronoun. This practice is only accepted in specific cases, and this would be one of them (because it is referring to a singular masculine person). 

If you'd like to learn a bit more on leísmo, here's an interesting Kwiziq article.

I hope this was useful.

Un saludo cordial

Inma