We took just this trip back in October, except that we rode coach. You will have the opportunity for lunch and dinner in the dining car eastbound, unless your train is extremely late leaving Houston. (I doubt you'll be needing this; the on-time performance has improved markedly in recent years, but I believe that it's still Amtrak policy that if the train is two hours or more late leaving the boarding station then sleeping car passengers can cancel without penalty.) On the return trip eat a good breakfast before leaving NOL; the diner does not serve breakfast and, at least on our train, the lounge car attendant took his own sweet time about setting up and did not open for business until nearly lunch time. You will get lunch and it is possible to have dinner; ask for the first seating and tell the steward that you're getting off in Houston. They will let you finish your dinner during the station stop in Houston, although I'd advise asking for your dessert "to go".
When in New Orleans we stayed at the Ambassador Hotel, which was an older property which turned out to have been nicely updated and was located only a block from Harrah's casino. I very strongly recommend the dinner jazz cruise on the steamboat Natchez; the food is very good and the music is wonderful.