I've just bought a shimano xt m770 9 speed mech to replace my half dead LX m570 mech.
No problems at all with indexing the old LX mech and the M760 shifter.
I put the newer mech on and I cannot get it to index. Either it shifts up the cassette fine and then struggles to shift down, or it shifts down, but then has problems shifting up. I had the same problem a few years ago with the same combo.
About half a turn of cable tension each way is the difference between it working one way on the cassette, but not the other.
No problems with the mech (straight, J wheels fine, springs good etc), jockey wheels are lined up perfectly and b tension is bang on.