"He likes his hotel."
Translation:Is maith leis a óstán.
It's the other way around; a/his lenites so for the consonants that can experience lenition you add an 'h' after the content. However, it doesn't have any effect on vowels (as lenition doesn't effect vowels). a/her doesn't lenite or eclipse, and as a general rule particles that don't do either cause h-prothesis before vowels. So to go over all possibilities, consider the three nouns lón, dinnéar, óstán.
his lunch = a lón his dinnear = a dhinnéar his hotel = a óstán
her lunch = a lón (note: can't distinguish from "his lunch") her dinnear = a dinnéar her hotel = a hóstán
their lunch = a lón (same as above) their dinner = a ndinnéar their hotel = a n-óstán