"What's going on, Lexie?"
Translation:Dè tha dol, a Leagsaidh?
If you look at the tips for the second skill, Phrases, it gives a good pointer to this. The letters that take the h after them are B, C, D, F, G, M, P, S, and T.
Words beginning with L, N, R, SG, SM, SP, ST, and vowels never do this. As tj4234 says, it's to do with pronunciation. So as Leagsaidh begins with an L, no h.
That is not quite correct. A lenited L is not shown in writing but there is a distinction in speech between a lenited and an unlenited (is that a word?) L. Gàidhlig actually has four L sounds:
The unlenited narrow L is like -ll- in English "million"; the lenited narrow L is like -ll in English "fill", so there is a difference in speech between the "l" sounds in: "lèine" (a shirt) and "dà lèine" (two shirts - lenited).
The lenited broad L is like English "fool" or "loom" (tongue behind top teeth), but there is no English equivalent of the broad L. (Try putting tip of your tongue behind your BOTTOM teeth and arching the tongue up to touch your top teeth!) So there is a subtle distinction in speech between "a làmh" (her hand) and "a làmh" (his hand - lenited). But PLEASE don't fret about this. The time to take Gàidhlig elocution lessons is after you have mastered drunken conversations in a taigh-òsta of an evening.
Yes, you are correct, the a' from a' dol runs into (or is swallowed up by) the a in tha. Where two vowels occur without a consonant between them the unstressed vowel disappears in speech. Depending on your views on what "grammatical correctness" really means, then even more grammatically correct would be:
Dè a tha a' dol, a Leagsaidh?
... but unless you were being very sarcastic or emphatic (or something) you wouldn't say it quite like that.
The a from a Leagsaidh is surrounded by consonants, so it stays.