Idioms – What Does ‘Count With’ Mean?

A meaning of split that is at least bordering on slang that means to leave somewhere, often quickly or without caring to tell anyone (see def. 13 here).

This party is boring. Let's split.

I haven't seen them around. They must have split.

So split town in this sense means to leave town. Split town itself isn't an idiom or well-known phrase.

Rock-a-bye has no particular meaning, though it's obviously patterned on lullaby, with rock replacing lull. Light songs and verses often incorporate nonce-expressions (expressions made up for the immediate occasion) and nonsense words and intruded syllables. They're intended not to communicate a 'meaning' but to create a rhythm or a mood or to establish a sonic pattern.

... be you blithe and bonny
Converting all your sounds of woe
Into Hey nonny, nonny —Shakespeare

Ob-la-di, ob-la-da, bra-la-la how the life goes on —The Beatles

They're particularly common in songs and verses for very young children:

Hey-diddle-diddle, the cat and the fiddle
The cow jumped over the moon

Once they've been created, however, these nonsense patterns take on a life of their own (the word lullaby itself probably started as a series of meaningless but soothing syllables), and it's not at all unusual for them to be employed as allusions to the work or genre from which they're drawn. Cole Porter, for instance, in his reworking of Shakespeare's Shrew as Kiss Me Kate, echoes hey, nonny, nonny very wittily:

With a hunny, nunny, nunny
And a hey, hey, hey
Not to mention money, money
For a rainy day
I come to wive it wealthily in Padua

In 1918 Al Jolson had a #1 hit with the song Rock-a-Bye Your Baby with a Dixie Melody, where rock-a-bye has taken on the sense "sing a lullaby to". And Eminem is doing something similar in When I'm gone. The song is about the conflict between the demands of his career and the needs of his daughter and estranged wife. The couplet you cite expresses this in the contrast between the two rhyming terms: "Slim Shady" is the aggressive persona he adopts when he sings to his audience, the persona which "made" him a star, "Rock-a-bye-baby" is the persona he strains to adopt at home, singing to his daughter.