Dates would help, but looking 2 wks and 2 months out shows limited availability in L.
May need to go via HKG. Some L class availability on some of the BA codeshares if you can book them.

2 weeks (23-Mar)
JL () 712 0 SIN 03/23/10 8:20 AM NRT 03/23/10 4:00 PM 777
C2 J2 D0 I0 Y1 B1 H0 K0 M0 L0 V0 S0 N0 Q0 O0 G0

JL () 710 0 SIN 03/23/10 11:20 PM NRT 03/24/10 7:00 AM 777
98% / 9m C0 J0 D0 I0 Y0 B0 H0 K0 M0 L0 V0 S0 N0 Q0 O0 G0

2 months (9-May)

JL () 712 0 SIN 05/09/10 8:10 AM NRT 05/09/10 4:15 PM 777
C9 J9 D9 X9 I0 Y9 B9 H9 K9 M0 L0 V0 S0 N0 Q0 O0 G0

JL () 710 0 SIN 05/09/10 10:40 PM NRT 05/10/10 6:45 AM 777
C9 J9 D9 X9 I8 Y9 B9 H9 K9 M9 L9 V9 S9 N9 Q9 O9 G0

Source: Expertflyer.
I recommend at least a one month subscription to help you search availability.