Translation:I walk in August but I run in July.
I think so, although here Lúnasa and Iúil are genitive (since they each modify mí) and need to become dative when following i (so Lúnasa and Iúil, basically the same forms).
On the other hand, if it had been i mí Mheithimh (there is lenition because it modifies mí, which is a singular feminine noun), where Mheithimh is genitive, it would have become Meitheamh, Meitheamh being dative.
EDIT: it should be i mí an Mheithimh, because Meitheamh means "midsummer".
Listening to these examples is an excellent way to learn the difference in the slender and broad "l." To me, it sounds like there is a slight diphthong, especially in the Munster speaker. If I practice "ú-uhl" and "ú-ill," I can feel the difference in the "l" (and then shorten the diphthong).