Flushed with victory, Lerian ran through the large rooms on the ground floor of the Palace, dodging servants who only half-heartedly tried to stop him, his bare feet slapping on the tile floors. The small grey cat that had been his constant companion from the cradle ran behind, mewing like a mother cat calling her kitten.

Lerian raced ahead, determined to be the first to bring the news to the one man whose approval meant the most to him, his father. The combat tutor, tired of Lerian besting all of the other boys, had matched Lerian against one of the guards in a wrestling match. And Lerian had won! He wanted to be the one to tell his father before the news reached him in another way.

Now, about this:

It seems to me that the first paragraph is completely superflous; The second would be a much stronger opening. I get the feeling that something bad has happened to the father, but you could definitely make this more clear with the foreboding. I have to get off right now, but send me what you've got written; I'll critique.

I like the flow. To me the sentences flow into each fluidly except for a couple of occasions.

The first paragraph, last sentence may I suggest '...ran behind, mewing as if calling a lost kitten.'

The second paragraph, second sentence:
'The combat tutor, tired of Lerian besting all of the other boys, had matched Lerian against one of the guards in a wrestling match.'
There are too many occurances of Leriam here. I suggest changing the second 'Lerian' to 'him'.

You don’t need ” that had been his constant companion from the cradle” just yet; that can be revealed later. Perhaps just say “his constant companion” so we know she’s not a stray and not part of the unfolding drama. Don’t need the second “cat".

Prefer this reordering: Lerian raced ahead, determined to be the first to bring the news to his father, the one man whose approval meant the most to him.
Suggest replacing: “He wanted to be the one to tell his father before the news reached him in another way.” With something like: His father would be so proud [this time?].

I do not sense any foreboding, but then I know where this story is going. Perhaps give us a hint that dad is hard to please, and junior may be heading toward disappointment yet again (if that is true). Otherwise I am interested enough to read on as-is; the action is enough of a hook for me. (The book's jacket already caught my eye )

What name does Lerian use when he thinks of "his father"? Father? Dad? You don't need it the first time, but I think it'd be better for subsequent uses.