It is simpler than that, in a way: words stay unlenited after "ar" in
certain set phrases. That's all.
If your sentences means "on a + some object or person", normally it is lenited. If the "ar" means something else than "on", then the following word may be unlenited. In set phrases, but set phrases are to be learnt by heart, but many are common and they are in the dictionaries

Btw, /hu:l'/ is the pronunciation of "shúil" (eye, with a lenition).
Quote:
A Lúghaidh, it is possible straightforward like that in Ulster Irish, and theoretically should be everywhere, but see IWM, paragraphs 382 and 383.
yes, it says exactly the same thing as me:
shúil is /hu:l'/
and
shiobhal (old spelling for siúl) is /x'u:l/...