As I wrote here, Lufthansa is my favorite program when it comes to booking domestic flights in business class, especially from LA to New York. This is because they are a Star Alliance partner and you can book United flights with LF's miles. Furthermore, United's new PS service from LAX and SFO to JFK has a new lie flat business class cabin for only 17,000 Lufthansa miles each way. Partner this with no fuel surcharges and a paltry $2.50 tax each way and you're looking at quite possibly the cheapest lie-flat redemption in the industry.
I just took this flight yesterday from JFK to LAX using my Miles and More miles and the combination of the In Flight Entertainment system, the food (tamale stuffed chicken was surprisingly good!) and the lie flat seating was an absolute steal at 17,000 miles.
Admittedly, 1,000 miles isn't going to get you very far on its own, but it could be the necessary bump to get you to the next level. For instance, Starwood SPG points transfer to Lufthansa's program at 20,000 points for 25,000 Miles and more miles. If you happen to have 40,000 SPG points, you can exchange them for 50,000 LF miles. Another 1000 miles from this promotion will allow you to hit 51,000 miles which is just enough for three segments on these business class flights I just mentioned (17,000 x 3 = 51,000).