I found three providers beside NXP that offer "out of the box" debug solutions for LS1043A / LS1023A:
Lauterbach:
Debugger for Cortex-A/R (ARMv8 32/64-bit) (LA-3743)
+ either PowerDebug Module USB 3.0 (LA-3500) or PowerDebug PRO Ethernet (LA-3505)
ARM:
DESTREAM-ST Debug & Trace Unit (DSTRMST-KT-0197A)
+ Arm Development Studio (DS000-KD-3x001)
Green Hills Software:
Green Hills Probe preconfigured for the NXP Layerscape LS1023A processor (GH-GP3-ARM-AC1-EUR)
+ MULTI Standard Development Suite for C/C++ (G-MC-ARM-IR-INT-PRM)
I had contact with a Segger support engineer and was told, that they can NOT confirm that J-Link supports LS1043A.
None of the above solutions have been tested by me and my team so far, so this answer is completely theoretical!